Sit and be fit on PBS was a good workout show that my grandmother used to do. Very gentle. Minimal, if any, strenuous exercises. If just being healthy is something you want for your mom (ie. more energy not necessarily losing too much weight) usually mild walks are a good way to start. Then there's resistance/weight training. 5lb-10lb dumbbells are good to have, along with some resistance bands. I know that's what my mom occasionally lifts at home. Body weight exercises are another thing. Modified push ups, crunches, hip thrusts, lunges, squats, etc. are good if you simply don't want to purchase exercise equipment. But I think the most important in "getting in shape" "getting healthy" "losing fat" or what have you is diet. Diet is ALWAYS key. You can be a few pounds overweight and find that you can lose that excess weight if you simply change what you eat, even with little to no change in your daily routine. Get her to eat better if she's isn't already doing so. I like to encourage a log of all the calories she's eating along with how much protein, fat, and carbs.
Again. You can do a search. She's not old. She can still do alot of the workouts you and I can do. Just modify it to her ability.
P.S.
I'm that woman you're talking about. =)