You might try JacksonGallaxy.com , the Cat Whisperer, he has what he calls "spirit essences" that help address behavioral problems. there is a shop button at the top.
Now, I have no idea if they work but there are good reviews for them. If nothing else they might get your purrbabies to the vet for the tranquilizers.

We have four cats and for the most part they get along fine. The youngest who is four would chase one of the older ones without mercy. They would make eye contact and the chase was on. He would also guard the litter boxes so he couldn't use them. I came across "Let's be Friends" flower essence. It only took a few days to calm the aggressor down.
I also like Rescue Remedy to calm anxious cats down.
To me it would be worth a try.

Here is a link that might be useful: Let's Be Friends

If you were able to put the cats in carrying crates once, you should be able to do it again. In this case, you only have to get the cats in the carriers to the vet's office. Once there, it's the vet's problem.

Get help getting them into a carrier. Having volunteered in a cat shelter, we often had fractious kitties who required 2 people to get them into a carrier.

Otherwise call vets, all of them you can find, until you find one willing to do a house call, and expect to pay for both the vets visit and travel time.

Probably too late for this advice, but, you may want to think about making the carrier less threatening. Rather than only pulling it out for vet visits, leave it out 24-7-365; make it a kitty home with a nice soft bed inside. I did this and would often finds my boys sleeping in their carrier.

Good luck.

I would be hesitant to have a groomer work on my pet while it's tranquilized. It sounds like your cats are older, which adds to the risk, so why not have the vet groom the cat while they have her. They can monitor her better if they have to tranquilize her and they may be better equipped to handle her without meds.

My previous groomer had the rule that if a pet was given any tranquilizer they'd refuse to groom the pet. An animal's reaction while on tranquilizers can be unpredictable and may become even worse during the stress of grooming.
If your cats haven't been neutered or spayed, consider doing that for a more peaceful household, otherwise consider finding homes for some of them so they can live out the rest of their lives in peace. It sounds like there's a lot of stress between the cats.

A tip that may help in crating the cat. First, place the crate vertically on its end so that the opening is at the top. Then, once you get a good hold on the scruff of the neck (have a towel handy for any flying feet) place the cat, hind legs first, into the crate.

Thanks everyone, I will call the vet tomorrow and ask if they will groom them there at the clinic.