Okay for what it's worth coming from a large and argumentative family myself, I think it's probably like this:-
You Mum wanted to go. It's no fun doing things on your own so she hoped that people she loved wanted to go too, and maybe cajoled them a bit more than some of them would like. To keep the peace you all went. You chose to take a smallish and therefore uncontrollable baby, and that inadvertently triggered a series of events that ruined her idea of how she wanted her fun evening to turn out. She got upset because you insisted on going and things were said and you then let the bomb drop that you didn't really want to be there ( and I imagine Linda didn't either because of what your Mum said to her). this has left your Mum feeling as though she was humoured, as though you didn't want to be there and consequently she feels disappointed and hurt. Go and make it up with her, life is too short (and no I don't think it's necessarily your fault, I just think it's one of those family things- we can argue to Olympic standard over NOTHING in our family) to harbour resentment over petty squabbles.