Option 2 without a doubt!!

I like the flow of Option2. Good luck.

OPTION 1, when you close a door the stripes wont go off under the door and make the room seem weird (hmm ... where do those lines go, like Alice and the looking glass ...)

Are you keeping physical doors (pocket or otherwise) between the rooms? If so, Option 1 for sure (which is also how it would have been done in adjoining rooms with pocket doors originally). If you're just having openings so that they're effectively very large continuous rooms, you can do it either way, I think.

If it's just the opening between kitchen and DR that's open without doors, you could also treat that as one large space---basically do option 1, but in those two rooms treat it as one rectangle and just stop and restart the pattern when you hit the wall stubs.

I'd also keep the Greek keys in the angled corners of the dining room whichever route you go, though.

P.S. I just went to look at how ours is done since we have an opening like that that's original to the house design---SO weird that I never noticed it before!

Our dining room and living room have trim exactly like your first photo, making complete double rectangles in both rooms. Our foyer, which is in-between the two rooms but open to both, has *only* the inner trim with the Greek keys---no outside rectangular border. It still forms a square that runs along the edges of the foyer, but that means that between the rooms, the pattern is Greek key-straight-Greek key (if that makes sense). Not sure that helps much, but it looks fine.

I still like option 1 best. I like how it designates space without walls- kinda like area rugs!

If I could ask- why are you replacing them? Good golly I would love those- maybe you can have them refinished????

I gotta say we just paid 10 a square foot out of a salvage yard to patch ours and yours look like they are in great condition. If you pull them up consider taking the wood to a salvage yard- take it from me- the good stuff is hard to find. Out of the 350$ we spent- only 1/3 of it actually matched after we sanded it a little.

Heather

#1 makes much more sense in my head. The floor looks OK...why are you replacing?

Ours was built in 1910 so it would be in the same time period and style of "Edwardian", but we don't have wood inlay floors like that :(.

Thanks everyone. I think we have the weekend to figure out what we are going to do with the borders.

Yeah - I didn't want to replace the floors - I thought they were fine. This is DH's thing - and it wasn't something he wanted to compromise on. He wanted to replace them now because they are very thin in areas and the floor guy said they would have to be replaced soon. Since we are doing a big remodel, it seemed to make sense to do them now.

I suggest option 1.5: Keep the front as original, in regards to the openings and where the border intersects the staircase; IMO another "french knot" would look awkward at the base of the stairs.
But, at the Kit/Dining opening, you are well within your rights to treat that as one floor, and not subdivide the spaces; even though the original wouldn't look bad at all should you choose that.
Casey

Okay, pardon my French, but your floor guy is an idiot. From the photos, your floors are fine--old floors are not like modern manufactured products--they are WOOD, not layers of ply on particle board.
I don't have any inlaid floors, but I had to cut an opening for a new register, and mine is oak over an inch thick, and has been sanded at least once judging by slight height differences around the registers--but--they could take a few more sandings and still not need replacing.
Looking at your pics, if you need any sanding, it would only be very light--I think your man has scented some easy money and wants to make a quick buck by replacing perfectly good flooring with something which won't last as long as what you've got, and won't look nearly as good.
The patina of your floors is great, and it would be a crime to junk it for a high-gloss gym floor look on the say-so of one person. Tell your DH to look at other aspects of the remodel and leave a quality feature alone. You will destroy the value of your house if you rip out original features!

I wasn't going to weigh in on this, but since columbusguy has put it out there, I agree---I'd absolutely get a second opinion on this.

Some older floors do need to be replaced; growing up we had an 1880s farmhouse that had sustained water damage on one floor and been sanded down many times, and those floors *were* thin. (Even those could be carefully sanded and refinished, though.) But it would be pretty unusual for a 1912 house to have floors wearing thin unless you've had standing water or have been sanding and refinishing them every few years, which it doesn't sound/look like. Before ripping them out, you might have another flooring person or two come out to take a look---you may be able to just replace a board or two, if there's a weak spot. Replacing them all is a pretty extreme action, if you haven't had extreme damage or wear (unless you're just doing it because you really hate the look---and it sounds like not, if you're putting in something similar). Old floors clean up extremely well with a sanding and a refinishing---they'll look like new, and will shine if you want them to.

If you're taking walls out, you may need to patch or replace in those rooms---but I wouldn't do them all just for that, though.

Thanks everyone for your suggestions and input -- I really appreciate it!