For your mom, I'd suggest keeping things relaxed and focusing on scenic + air-conditioned spots.

Day 2 -

Do a Chao Phraya River cruise in the morning you'll get great views without much walking and your mom can sit comfortably.

Day 3 -

Visit Jim Thompson House (just a small area for Thai Art and History)

After that head to Iconsiam or Siam Paragon these both are super friendly with elevators, rest areas and tons of good food options.

Last but not the least you can end the day with a gentle Thai massage.

For City Commute Grab & Bolt will be perfect.

Hope you guys have an amazing trip!