I think it's a great idea. Not only would it mean a lot to her to see you happier and healthier, but it would also give you a reason to stay focused and consistent.
If you decide to go for it, just remember to start thinking/planning for how you'll live/behave after your mom returns. If you don't include that, chances are the weight loss will be temporary.
Best of luck to you and sorry to hear about your grammy!