You have very unique needs. Have you considered finding an architect to design a house that will work for your special needs?

I'm not usually quick to jump on the "you should get an architect" bandwagon, but, in your case, I don't think you're going to find anything ready-made that's going to fit your very unique needs.

Specific thoughts on your requirements:

Open floor plan – we have two children with disabilities and they
use walkers and/or wheelchairs to get around. Every door opening needs
to be at least 36 in. wide.

I think this is your easiest requirement. Open floor plans are very much "in style" because they are less expensive to build and require lesser square footage. As an extension, I think you should think carefully about your eating area ... plan it so that two wheelchairs could "pull up to" the table.

4 bedrooms, master, and three kids bedrooms. We’d like the kids
rooms to be at least 12x12, without the closets being in the rooms.

Standard twin beds for the kids? Where do you see the closets? Opening from the bathroom, or a family closet off the laundry?

Tread cautiously here ... lack of traditional closets in bedrooms could be problematic if you're borrowing, and they could be the kiss of death for resale.
Preferably 3 bathrooms, one in the master, one for guests and our
daughter, one of the bathrooms needs to be fully accessible, tiled
shower with no transition, something they can roll into and has enough
room for one of us to help them while in there. We’d like it big enough
for a table for one to lay on, they have incontinence issues and where
diapers. This may be a jack and jill set up.

I think the kids' bathroom may be your most difficult item. Have you seen wheelchair accessible showers in nursing homes, etc.? Consider a Tornado Body Dryer; they allow you to dry off after a shower without a towel. Consider storage space for the diapers, etc. How old are the children, and will they need to lay on the table as they grow? Could this table be a part of the vanity? I usually like a jack-and-jill, but, in this situation, you're going to be involved in the toileting ... and you might not like to go through the bedroom every time you need access to this room. I also think it'd be important that this bathroom isn't visible from the main living areas. Personally, I'd be glad to sacrifice bedroom space for bathroom space.

A large mudroom room for the shoes and different accessories we
have such as summer clip on fans for the wheelchairs to winter covers,
shoes for wearing with leg braces and those to wear without, etc.Yes, for a while my grandmother used a walker when she left the house ... but didn't use it IN the house. So she needed a space near the back door for her walker to be stored. I can see that you'd need a good sized mudroom with well-planned storage.

Something my now-RN daughter liked when she worked in home health: She liked it when the family set up an information basket for her near the back door. Typically such a basket would contain a clipboard with notes from previous home health care workers and contact information for the family. You might consider a spot in your mudroom where you could have such information for any home health workers who might visit your home now or in the future.

Another thing she mentioned was that all her clients -- they were adults, not children -- seemed to enjoy sitting in a place where they had a nice view of the outside. One lady she worked with lived in a horrible tiny house, and she insisted that her wheelchair be placed in the front door all day long so that she could look outdoors ... even though it was very inconvenient for her family.

The other thing my home-health daughter would say to you: Consider fire safety. She's big on that.

A ramp preferably in the mudroom as well, but if not then in the garage, this is a must.

What I'm hearing you say is that you need one good, comfortable entrance for the kids. Be sure it's covered /out of the elements.
A good master suite, large shower and walk in closets, we need a retreat area.

I like the plan above that has a sunroom off the master. It was arranged so that the sunroom was accessible from the main living area AND the master ... looked ideal.