This is a situation many parents will recognise and it can be tricky to negotiate.
You are right to approach this with caution, but if you can help her think positively about fitness now, when she is young, you will be giving her a gift that should last a lifetime.
Firstly, if you can find an activity or two that she loves and that makes her smile then she will be exercising without realising it. That’s a major first step. Does she dance around or do Karaoke when she is with her friends? Then perhaps organise Wii parties for them.
If she likes swimming, walking the dog, or bowling, make those things regular fun, family-time sessions. When you have your mum-and-daughter chats, resolve to do them outside, while walking around the block. Small steps lead to good, long-term habits.