Scarlett, drywall will not be able to bend to duplicate the coved ceiling; you will be better off taking down ONLY the plaster which is too loose to reattach. Lath and plaster is a far better insulator sound-wise than drywall, and is more durable.

You don't need to take down the lath to fix plaster--just remove the plaster that can't be repaired with screws, and do several coats of new plaster. To make it a little easier, you could attach drywall to the lath, to bring it up to just below the depth of the surrounding plaster, then skim coat it to level the two surfaces.

Maybe paint remover for the bath?

It is sometimes hard to keep up the enthusiasm, but keep picturing the end-product, and you will persevere. Bear in mind that what you are preserving cannot be replaced today, and is far better material than used today in similar sized homes without spending a ton of money. If you get down, tackle one small project--say painting a room--and seeing that done will keep your spirits up.

If all else fails, go out in the yard and plant something...or prune something...or just enjoy a grilled burger or dog--sometimes a change of scenery can do wonders.

regarding the ceilings: lath and plaster is the best wall / ceiling material out there, so save it if possible. pictures are necessary for better help. why is the plaster falling down? water damage? small repairs (cracks, smaller holes, etc.) can be done with mesh tape and drywall compound. make sure you have the right tools - this includes high quality drywall knives of varying lengths (some people swear by plaster trowels). larger damaged areas should have all plaster cleared and drywall cut to the opening, then tape and mud the seems. after doing all the repairs, skim coat everything, prime and paint. it will look beautiful if you take your time.

if the whole ceiling is a total mess, the best option would probably be to just demo the plaster and put up drywall. this will be a giant mess, but it is doable.

"We have been advised" to take down plaster.... who advised this? Bear in mind that that is what a lot of people will advise, simply because drywalling is what they do and what they know how to do.

There is no reason to ever take down plaster unless there is severe mold or it is literally falling off as may have been the case with your ceiling. Even then if the falling away area is not too large you can repair it with plaster washers to reattach it to the lath, or if you can get behind the lath theres ways of reaatching the plaster keys to the lath.

Ceilings are often most problematic because of gravity. Walls not so much. Cracks and loose areas on a wall are usually easy to repair. You need to find someone who loves old houses and knows the whole repertoire of methods and fixes ... instead of the one trick pony who only does drywall.

if you can get things stabilized and taped, so all that needs done is covering the cracks and then skim coating, the one-trick drywall pony can do a fine job from there and for a lot less than an extremely rare plaster guy.

Before destroying plaster make sure it cannot be repaired, and ten price out new plaster (at least two coat) to estimate what you are throwing away.

It has far better sound attenuation characteristics than anything except multiple layers of drywall.
Even drywall the same thickness as plaster is not as good.
The stiffness and weight of plaster is much better.

It can be worth repairing damaged plaster and THEN covering it with a layer of drywall to create a new smooth surface.
The repair does not have to be as perfect (and in many places drywall installers and finishers are a lot easier to find then plasterers.

You do not have to use plaster and lime putty to make repairs to plaster walls.

Setting type joint compound is very effective.
Easysand if you cannot work the material well, Durabond if you can (Durabond is as hard as actual lime putty plaster and does NOT sand well).

Most of the stuff sold as patching plaster is not worth even trying.

We have been working on our house for 25 years and are finally almost done. If you get discouraged or burned out, just remember that you do not have to be working on it all the time. Take a break. It will still be there when you get back. We have lived in our house for 18 or 19 years, and it was a long way from being finished when we moved in. Sometimes we would get so burned out we would take a year or two off from working on it. We didn't go anywhere (couldn't afford to), but just had a couple of rooms we could retreat to that were done. The rest we would just ignore. Rome wasn't built in a day! We both had the ability to not see everything that was undone. Like right now, the back stairway needs the wallpaper removed and will need lots of plaster repair. I don't want to have a plaster dust mess again for awhile, so it will probably be at least a couple of years before we get to it. I know, some people can't live like this, but if you can, it really helps!

You've gotten some good advice on the plaster thing. Not sure about the bath, some pics would help.
As for keeping up your spirits. It's helpful to take pics of all your projects BEFORE you start them and then at different stages. Looking at the pics sometimes can be inspiration enough to keep you moving forward. At the very least will remind you that you have made some progress, something that is very easy to forget when you are working on such a large project. It also creates a nice brag book to show of to your friends when you finally are done.
Don't become a slave to the house. Yes, it'd be nice to be done with all the construction and mess quickly HOWEVER you have a life and you need to live it. The house didn't fall apart in a single day. It took lots of time and it's going to take time AND money to repair and update what's been left undone by PO's.
Most importantly you need a sense of humor. If you can't laugh at some of the stuff you are going to have to deal with, with a old house you are going to spend a big part of your time crying and ultimately hating the house.
Laughter can take the stress right out of a bad day. You just need to be smart enough to find the humor in the situation.

How you do the project has a lot to do with the mood you sustain throughout. If you have a house that really needs a total systemic redo (gut and replace) and instead you are just dabbling here and there with cosmetic upgrades and never really tackling the causes of your problems from the ground up, it is like plucking hairs from a yak and you may get discouraged with good reason - your methods aren't matching the scale of the task at hand. Now, sometimes people do get into a house that is too much for them - ask me how I know! But assuming your projects are the ones most needing to be done, it is easier to be enthusiastic when you are really gutting a disaster and redoing it properly - say, replumbing a new bathroom rather than just adding some more pipes to the Krazy Plumbing From Hell and 7 previous owners' amateur efforts, or stripping six layers of paint rather than simply adding a seventh.

Conversely, it can also be really overwhelming if you want to do it all thoroughly because that means each job takes a long time. What I would say in retrospect, having lived with ugly/grungy/unfinished for a long time, is that there is nothing wrong with at least slapping a coat of paint over the old stuff you aren't quite ready to get to, so it at least looks charming, and you can test out paint colours, until you're ready to tackle the whole job.

Regarding lath and plaster, there is a time and a place for purism. We did not find ourselves there, because our plaster was more or less crumbling off the walls and we live in an earthquake-prone area. Throughout the old part of the house, we took it off and did drywall, some over lath and some not. I did try hard to rescue one room's plaster, but there was truly no hope. You may have better plaster, or indeed be able to get replastering done. It was not in our purview. If you do drywall, you can do the coves somehow; put up narrow strips of drywall along the curves and fill between them.

On the bathroom wall, a skim coat of spackle may be your friend. Not all paint needs to be removed. Funniest thing I keep realizing too, is that one thing that quite reliably softens old paint is a new coat of paint over it. I frequently encounter ridges and drips of old paint, and at first I used to chip away at them with little success. Then I gave up and just painted over them, only to find that once the new paint had dried, the paint underneath became butter soft (almost) and could be carved off much more easily. You won't be able to scrape off layers of it though, so if patchy layers are your problem I would do a skim coat.

Post a photo or two if you want more specific advice on any of your questions.

KarinL

1. Drywall
2. Gut the entire bathroom and do a total rebuild.
3. Work one room at a time from top to bottom if possible. You will feel better having a place that is completley done, and not have to revisit it 6 months later. Been working on mine for ten years, each time I complete a room or major project it motivates me to take on the next one.