A great train option if you want to joy ride - go to Union Station and take the Amtrak Pacific Surfliner to San Diego. Frequently service (approx hourly during the day), great views as significant sections of it run along the coast, the trains are bi-level so you can sit high, plus you can do a quick trip into San Diego while here.
Santa Monica Pier - worth going to. They have a small amusement park on the pier, and it's fun to walk out and watch people fish and do other things. Also, it's right on the beach, so you can visit the beaches of Southern California.
The Venice boardwalk might be a good option too.
Travel Town would also be good for a kid who likes trains.
Universal Studios is another option.
Note that if you do go to Disneyland, your mother can get a wheelchair. Most rides are accessible for people in a wheelchair, especially since it sounds like moving from chair to rides wouldn't be an issue at all.
FYI, if you want to same some money on getting around, there are a few good options providing east-west service from Beverly Hills, as the taxi trips wouldn't be cheap. Depending on where you are, you would likely want to use the 4/704 on Santa Monica Blvd, or the 20/720 on Wilshire Blvd, which both provide frequent service into downtown Los Angeles and Santa Monica.