Know of any fun activities to do with my mom?

There are different chain shops that give you plates and allow you to paint them and then they fire them for you.
Zoo
Park
Movies
Bake cookies
Paint each other's finger nails
If you like sports go to a basketball court, tennis court, or whatever you would enjoy playing together.
Since she's taking you all shopping ask her what she would like to do. She would likely be happy that you care enough to want to do something that all of you can enjoy.You may also try
touring gardens and going to a pick your own fruit farm

When my MIL lived here, we used to look at magazines together. We had some that we both enjoyed and it would prompt discussions on home decorating, fashion, etc. and stimulated conversation. It was interesting and fun. We chose some recipes and crafts that we were going to do together.

Also, I bought some old movies from her era in the 40's and 50's that she enjoyed and we would watch these together.

I might start thinking of things we did together, when I was a child. Bake cookies? Play Dough? Play her favorite songs, jigsaw puzzles, etc.