How can I help my parents with mobility when I have health problems limiting my strength?

Thank you everyone for your helpful suggestions.

I had not even thought of asking their Dr. For an in home assessment by a physical or occupational therapist. That would be a very good idea.

We have a commode, I will have to see if it can fit around the toilet. That would save them having to buy a toilet safty frame, i think it would be just as sturdy.
That would be very helpful. Especially when mom has vertigo It may make her more secure feeling as she would have the arms to hold and reassure her she is not falling off if I have to step away to get something for her.
It's funny how I didn't even think of the camode... it's just sitting right there in the bedroom, and it could be easily moved back and forth to the bedroom when needed in there :-) I'm I newbie, Lol!

I was looking at the space in our bathroom, I think a small wheelchair could be manouvered around. I could wheel it in and leave the door open while getting mom from it to the toilet, then turn it around and it would be ready for her to get in and leave the bathroom.

A friend was showing me that they had moved their walker wheels to the inside recently that seems like a very good idea.
I will have to get out the measuring tape and take it with me to look at walkers and wheelchairs (or make sure any I get online can be returned locally if the measurements are not as described...)

Thanks again everyone!

JWdaughter, you mention that your Mom get vertigo. Ouch, that can be rough on anyone no matter what age. My own Mom had bouts with vertigo and found using "anti-vert" really helped her. Today, one can only get the generic form and it is fairly good. See if this is something that your Mom's doctor would approve. It is really worth a try.

Our regional hospital has these plastic wheelchairs which are easy to use. The wheel brakes are at the back of the chair. I tried to look for one on the internet but couldn't find it among the 100's and 100's of wheelchairs posted. These are white with a light blue seat.

When my mom was having OT and PT at my house, the PT took the wheels off the walker and reversed them so the walker would fit through bathroom door...that was his recommendation.

My mother sits all day in a lift chair that has a motor and a remote. It lifts her up and tips her forward when she wants to get up. Her bathroom also has a narrow door and even her walker doesn't fit in, so she holds onto the sink and grab bars to support herself getting into the bathroom and on to the toilet. She has what's called a "toilet safety frame" which essentially puts grab bars on the sides of the toilet that she can use to help herself up.

With a wheelchair, you have to consider not only the width of the door but the space inside the bathroom to maneuver the wheelchair. It's tricky to turn a wheelchair in a tight space, especially with someone sitting in it. Pushing a wheelchair does take strength, how much depends on the type of wheelchair and the weight of the patient. The transport wheelchairs with the small wheels are lighter, but with a heavy person sitting in it it's still tough. My mother weighs 200 lbs and I can move her fairly easily on level ground -moving up a wheelchair ramp and over raised doorways takes some oomph. I would not recommend it to someone with compromised upper body strength, in all honestly.

When I lift my mother, I use my back. I lean over her, have her put her arms around my neck, grip her around the waist, and stand up. A lot of times I have to hold her upright for a minute or so while she gets her balance before transferring her to her walker or wheelchair. Maybe this maneuver would help you if your back is stronger than your arms.

I would consider asking your parents’ PCP for a home care order specifically physical and occupational therapists. They will come to your house and do a home assessment and give you suggestions on how to transfer your parents, equipment you may install to assist them to assist you, etc. Homecare won’t last too long  but their visits can provide you with a lot of good information. Medicare & their supplemental insurance  should pay for this as well. 
Good luck!