How to handle MIL wanting to join all my activities?

My MIL is a really nice person but I’ve always struggled to get close to her. I’m not sure why but I never felt comfortable opening up to her about even the simple things. A few years ago we moved to the same city as them which was fine and we met once in a while to hangout. But I know she wants to connect with me and she’s told me she always wanted a daughter. In the past few months, she’s somehow joined my gym and now she’s joined my monthly activities at the library which I joined in the hopes to make friends. And now she texts me that she’s so excited and can’t wait and I feel like I’m obligated to sit and talk to her when I want to be able to move around to different seats each month to meet new people. This has given me anxiety almost everyday because I don’t know if I should just drop it completely or somehow tell her I don’t want to sit next to her and hurt her feelings. How would I navigate this situation? I know she wants to get closer but I don’t feel a big connection and every conversation just doesn’t come as naturally as it would with other people and now with this I feel like I don’t even want to make small talk anymore. I’m not sure if I’m being mean or if it’s ok to just want some independence and not the same type of relationship.