How do you ask your mum to be more involved in helping with the baby without hurting her feelings?

It depends. For me personally I try not to ask for help too much as my kids are my responsibility and not theirs. But for urgent cases, I'd just bring it up to her and see if she's okay if it. If she is, good for me so I wouldn't need to seek external help. But if she's too tired, then I'd engage a part time baby sitter.