OY! Mothers!! (Yes this IS cycling related)...

[DDH]

Here's a story for you.
My Stepmother who is in her mid 50's started riding a big heavy cheap bike she bought from the px last year, back and forth to work. She was very heavy and 2 years ago had gastic bypass surgery and after losing over 100 lbs she started riding this bike. I still had my mountain bike and had started riding again last summer after I quit smoking and was trying to get into shape and lose weight, so her and I started riding together off and on last summer and let me tell you, she kept up with me just fine on that heavy clunky bike. My DH and I told her several times that she would be amazed at the difference if she bought a better bike, but she did not want to spend a lot of money on a bike when she wasn't sure she would stick with it and that is why she bought that one.
Well, last summer was when I got my new hybrid Cannondale so I sold my Stepmother my mountain bike (cheap) since I wouldn't need it, so she could have a better bike to ride and we all went to the Waco wild west organized ride last year and she and my dh made it the 50 miles and I didn't. I sagged out after I think 30 miles and just couldn't go anymore. I went back to the truck and waited and they both came in dog tired and ready to collapse but they made it.
I guess that big heavy clunky bike, prepared her better and got her in better shape, so when she got my better bike with the street slicks it was much easier for her to ride. At least that's how I justify me not making it and her beating me. LOL

Point being I guess, encourage your mom to ride the heavy cheaper bike and help her get the best fit with it she can, and when or if she falls in love with riding, then help her find a good bike that will last for her and fit her even better and she will be able to fall in love with riding all over again. I thought the same way as you about those cheap bikes, but my stepmother did fine on hers and I understood why she didn't want to spend a lot of money unless she found out if she was going to enjoy it.
Just think if she gets good on the big heavy cheaper bike, how much better she will be if and when she gets a good bike. Let her know she can always look around for a used one so she doesn't spend so much too.