Wheelchair vs Walker

No one can give you a good answer because we don't know your mother. The answer is based on what happens, now, at home. (Note that the following discussion is based on Manhattan, NYC residence. No SUV and Mall-Walking is involved. Pure pedestrian life.)

My 93 year-old mother, with severe cognitive deficits, is strong enough to walk 1/8 mile. Sometimes. If I knew that I could not tolerate (time-wise) a rest every city block, I would take the wheelchair. She is actually willing to use the handles of the (Walgreens transfer-chair, $110 more or less) as a rollator. But when she poops out, she just sits down and gets pushed.

This is about you, too. You did not say if she resists the wheelchair as an insult to her abilities.

I would note that a transfer chair (which has smaller diameter wheels, the issue) on cobblestones (which are much more common in Europe than in the USA) would not be as easy or as pleasant a ride for the patient. If the footrests come off by design, you need to handle that before checking the chair. I'll bet you could buy a new chair in Amsterdam (paying VAT, of course ... ) if anything bad happens in the baggage hold.

I don't know what type of walker she has, but if you don't have one, invest in a Rollator.
She can use it as a walker and it doubles as a small wheelchair. They collapse easily for travel and are very comfortable and usually have storage under the seat .
Unless your finances are strapped, go with tours that accommodate your needs. It will make for a much more pleasant trip for both of you.
I don't know your circumstances, but consider making the trip memorable for the both of you over the cost.

"but limits on the airplane may matter" You used "may". Does that mean you have not contacted your airline for the specifics?
I've recently flew on Southwest and saw a wheelchair getting loaded into the baggage hold. It was the last item to be loaded after all the suitcases, so presumably, the airline took some care in handling.
However, I agree with the other posts that a rollator would be easier to transport. Amazon has several models under $100.

Actually, I'd bring both. Both have their purposes and they both fold up. Check with the airline to see if you can check both at the gate. If I had to chose one, I'd chose the wheelchair as no matter how tired she becomes you can keep going. The collator and her limited mobility would impede any real site seeing.

Possibly you could rent a wheelchair.