Any ideas for getting Mom out of her transport chair and into my car?

I used a heavy duty contractor garbage bag with the end cut off so it was like a giant flat tube.
Place the bag on the seat of the car.
Have Mom sit on the seat once she is properly positioned.
Move the walker out of the way and grasp her feet and ease them into the car while helping with your other hand to turn her in the seat.

The plastic bag makes it very easy to mover her around on the seat. It also makes helping her get out a bit easier since you can more easily turn her in the seat so she is sitting on the seat sideways. Once she is on the seat sideways move the walker into place, lock it and help her to a standing position. It helps if you have a gait belt around her though, should have one anyway just for safety.

They make padded seats that are basically like a lazy Susan that we used with my mom. Once she sat down on it on the seat, it was much easier to pivot her around and get her legs and feet in front of her. Same for getting out. I got mine at Walgreens I believe.

The metal handles that attach to the door jam of the car also worked well as someone else mentioned. That way, your mom can have handles on both sides getting in and out.

If she stands in the walker, can you ease her back into the car seat with the instruction “Sit down” when the SIDE of the car seat is against the back of her legs?
Once she is sitting on the car seat with her legs at the side, you can pivot her feet into position in front of her.
This was a technique recommended by my mom’s PT, and I would assume any PT or OT could show you.
My mom was a chunky 4’11”, and it worked well for her.
Please forgive my poorly worded explanation.

My mom has back, hip and knee problems (one hip and both knees are replacements) and we have some challenges with the sit and pivot technique. Mom can still do the "sit" where she's in the seat with her legs against the side; it's the pivot that is challenging. We found it is easier to have a slidable car seat surface (folded polyester satin sheet), a car with a higher seat if possible (seat in minivan or some baby SUVs is a few inches higher than a sedan), adjusting the seat to the all back position and reclining the seat back if possible. Pushing the seat back gives more room to maneuver the legs; having the seat reclined allows mom to lean back and use her hips to compensate for knees that don't bend much beyond 90 degrees. After she's in, we raise the seat back because she doesn't like the recline position for driving around.

When my sister needed help standing and getting into the car during her cancer battle, we found it easier to get her into the 2nd row seat of my minivan because the sliding doors were out of the way. We could roll the wheelchair up beside the car seat. I could get her up with a forearm under her shoulder. She could put an arm over my shoulder and brace the other arm on the front seat back while moving into the car seat.

All of these are great suggestions. I recently faced a similar problem with my 95 year old uncle who is in a NH. We wanted to take him to my Mother's 98th birthday party. I used a gait belt, which does have to be very snug, and a stand and pivot maneuver to transfer in and out of the car, very similar to a transfer from bed to chair. I also purchased a transfer board from Amazon which I believe would work very well with a transport chair that has a removable arm (my uncle's does not). My uncle is able to follow directions so this made it simpler when I was able to direct him to stand, turn, sit. Once I transferred him to the chair, I used portable ramps that I purchased online to just wheel him up the short stairs into the house. I recommend being very familiar with good body mechanics to avoid injury to yourself. I am an RN and it makes all the difference in transferring patients.

It would be easier if the transports arm came up but I doubt yours does. Then you use a transport board to slide her in. My problem was my car seat was just a little too high and eventually Mom became dead weight and we had a hard time getting her in. With the Dementia she was no help. Couldn't take instruction. I am 5ft tall and if alone, there was no way I could take her anymore. I cut back on doctor appts, some I dropped because the reason Mom started with them her primary was able to take over the care.

Are you using a gait belt? These can be a great help with transfers.

I found the main difficulty was positioning myself, the chair and mom in the space left available by the open car door, although perhaps a larger car would make a difference. I personally never had much success with the gait belt because it seemed to need to be impossibly tight or it just ended up sliding up - I did much better using the waistband of mom's pants as a place to grip and lift. The technique involves as fairly basic pivot transfer - stand, turn, sit (with the legs still outside the car), the plastic bag on the seat really helps when you put her legs in and spin her around facing forward. I had to face the reality that we just wasn't safe to try it anymore once mom couldn't be trusted to consistently bear her own weight long enough to pivot from the chair to the car.

If your mom is used to “reaching back” to grasp chair arms before she sits, I purchased a metal handle grip (Amazon) that hooks onto the frame of the opening of the car door and is used for her to reach back and hang onto before she sits down. She would grasp the open door arm rest with her left hand and the temporary metal grip with her right, then sit down. This helped a lot.

I bought $1.00 bandanas and tied them around the medal poles that hold the headrest. It's almost like a pulley. When she holds on to them, she can hold tight and pull some of her weight to get in car. With my help it is easier for her to get in car.