Difficulty walking to the bathroom. Does anyone know of some sort of mobility chair, like a wheelchair but smaller and more maneuverable?

It's called a "transport chair". You are so wise to seek out this information.

Before you order one (see if her doctor will script it so Medicare will pay for some of it) make sure to neasure your doorways and the turns.

I'm going to suggest an OT come to your home for a consult, they can be so helpful in pointing out potential obstacles and knowing about solutions. Be sure to have a list of questions to ask in order to get the most out of this, include any difficulties you have encountered with bathing, getting in and out of bed, eating and meals, etc

What about a walker with a seat? It might be just small enough that if she can hold her balance in a seated position, you can gently push her the way?

https://www.amazon.com/Medline-Rollator-Rolling-Supports-Burgundy/dp/B079PG3BR3/ref=sr_1_9?crid=9CMRSETYVJ2R&dchild=1&keywords=walker+with+seat&qid=1633025315&sprefix=Walker+with+se%2Caps%2C199&sr=8-9

Just got a Medline Ultralight Transport Chair through Amazon. It comes assembled, but folds to store in the car. It's 23" wide and fits in the doorways of our home. My husband's wheelchair was also too wide to wheel him into the bathroom. The local med equipment store said they can't get these in stock. Hope this helps your situation.

There are walkers that will fit through narrow doorways. I found one for my Mother on Amazon.

ProBasics Junior Folding Walker for Seniors - Sure Lever Release Folding Walker, for Petite Adults. JUNIOR SIZE, LIGHTWEIGHT WALKER. The mobility walker is very light and maneuverable and has sides that detach for storing in tight spaces. Walker only weighs 6 pounds.

Also you might consider hospice for your wife. I suggest this as dementia is an incurable illness that Medicare provides hospice care for. If you have her assessed by a hospice agency they will know whether or not she qualifies at this time and help you get the doctors orders. With hospice they will provide all the durable equipment she needs. A gait belt which can help you when you transfer her, a rollator, a transport chair, a bedside commode. A hospital bed, the appropriate rails and mattress. Plus should she become incontinent they will provide those supplies.
My DH aunt is on hospice for over a year now. They send a weekly nurse and bathing aides. This help could keep you and your wife managing for a longer period of time.
If she doesn’t qualify for hospice yet, the next step would be to check with home health for the homebound. She would qualify for that depending on your insurance. Again the home health agency will know if she qualifies and help with the paperwork. Similar durable medical equipment is available through Medicare only instead Of it being loaned by hospice suppliers it is rented by Medicare and they pay 80% and you or your supplement plan pays the other 20% for a set number of months and then it belongs to the insured.
With either of these programs you would receive a lot of help and should your wife need blood work or UTI tests, these can also be provided.
You sound like a wonderful husband and father. Wishing you good luck on getting the services your insurance provides.

I had the same problem with my wife. I removed the bathroom door and was able to get her wheelchair, with her in it, into the bathroom. You would have to remove the bolts from the hinges that hold the door on. that eliminated any bathroom privacy for family visitors, but they didn't seem to mind. I don't know whether that would give you enough room to get your wheelchair in, but you might try it.
All of the answers so far seem very helpful.
The rollator walker suggested by Lizbitty is a great idea, but it looks like the one on Amazon has the seat in front of the person using it, which means she would have to turn around to use it. If you can get your wife onto that seat from her bed or chair, that may work for you. I spent hours looking for a walker with a seat that is behind and under the person using the walker, but only found one. The cost was about $800 and it was too rickety to risk using it. Best wishes. I hope you find a solution.

A walker is narrow enough, or a rollator (transport chair). Both are covered by Medicare, with a doctors prescription. Having an OT to assess her would be great, as was suggested earlier - to get the perfect aids for all her needs right now, as well as teach you and your wife how to maneuver around the house. Best of luck!

They have smaller width wheel chairs plus they have transport wheelchairs that are smaller in width.
Also, some find it easier to remove the door off the bathroom for easier access.
Of course in the future when needed, you can buy a bedside toilet that can be located anywhere close by so your wife only had to shuffle a couple feet.

Shop with a measuring tape and, if possible, go to a specialty store. My Mom lived in an older mobile home and the doors to the bath and bedroom were VERY narrow. We did find rollators and one transport chair that were small enough, but it was a struggle.

Please write to your state congressperson about changing building codes to require a minimum of 30 inch doorways to all rooms in a home. The long-outdated 26 and 28 inch doors are a nuisance to young able-bodied people as well. They are very awkward for getting things in and out of rooms. I lived in one house where the bathroom doors were further cut down to create 24 inch doors. Boy did I learn to hate those stupid things every time I went through the doors with a pile of towels.