Looking after an energetic two year old is exhausting even for a young mum never mind a not so fit grandmother. If mum is not fit for the job could you offer to help her at home for an hour or two and then take the little one for a walk or home with you for an hour so that mum can sleep. Maybe you could do this two or three times a week and the little one could go to nursery the rest of the week. A fair compromise for two years until school starts to keep the peace and to keep your bond with your grandchild.
If that’s more than you can cope with then you need to say so.
Be strong and good luck.
Widows and divorcees - and kindness