Sorry this is long, it probably seem something and nothing but it is getting to me!
Mil is quite a controlling woman - she loves being a gp but can be quite opinionated. Fortunately, we share similar opinions on most aspects of child-rearing, though she has made comments here and there, which I have tended to smile and ignore.
The main 'problem' (though it hasn't really caused and huge problem as such, yet) is that when she spends time with the dc she likes to be in charge and dominate them. I am f/t wohp and dh a sahd so we have mainly got around this by her seeing them while I am at work - thereby giving dh a little break and not annoying me!
When ds1 was about 6 months old and I went back to work she said she wanted to take him to swimming lessons. Now I can't swim 
and dh was new to being a sahd then and unsure about whether he could/wanted to take ds to the parent/ child sessions, so we agreed. I will admit I felt a little put out about it because I felt that she wanted to have a 'project' with ds - it wasn't enough for her to visit him, she had to be the one to teach him to swim. I told myself I was being silly/ a bitch and the swimming lessons went ahead, with much fanfare from mil.
Ds was always a little lacking in confidence physically and I became aware that mil was having problems getting him to join in with some of the activities the class were doing - splashing/etc. She was never horrible about it but she did make several comments comparing him to other children and this annoyed me. I raised it with dh and he felt I was just jealous of his mother taking ds swimming, there may well have been some truth in this so I let it drop.
Another annoyance was that I am a teacher and she continued with the lessons during the school holidays. This was ok in itself (though I will admit a couple of times I deliberatlely accidentally arranged other stuff on those days so it had to be cancelled) but she lives a 90 minute drive away, suffers from insomnia and the lesson was at 9.45am. She would arrive right at the last minute, in a complete flap and bark orders at me about the stuff he needed. It was a pain and I began to think if it was so hard for her why didn't she just drop it? We never asked her to take him. It became clear dh felt the same as I did as when I mentioned her lateness/stressed manner he agreed and said he was worried it was too much for her.
Fortunately, I then went on mat leave with ds2 and it all fizzled out a little and then ds turned 3 and too old for the accompanied classes anyway. We considered starting him on the next classes but money was pretty tight when I was on mat leave and it was not our priorty. Since then (this was over a year ago) mil is always on at us to start him on the classes saying we 'really must get it sorted' and asking whether we have 'managed to sort it out yet' and sighing heavily when the answer is 'no'. The thing is, we have looked into it but I really don't see any hurry. I have done some research and it seems to suggest that most children aren't physically ready to swim before 7 and he will get lessons through school before then, right? He and his brother do 2 other classes - both of which they asked to do and love and to do a third seems an expense we could forgo - or AWBU?
The thing is, now she has said that she is going to start taking ds1 to swimminng lesosns again - why???? Why can't it be our decision? I feel she has decided that we are so irresponsible we were never going to get around to it and it has all been left to her yet does he really need to swim now? I say no. I am also annoyed that she doesn't offer to take ds2 to the same classes she took ds1 to. Imo, that would be the more logical step and would mean she had treated them both equally but instead she has this obsession with ds1 swimming but couldn't care less about ds2! (Btw, I don't expect her to take ds2, just feel it would make more sense than what she is proposing.) Also, I am not sure how she would deal with any reluctance on ds's part (I am sure there would be some because he would be nervous) and just feel that she may handle it in a way dh and I would not be happy with - I'm not talking about endangering him, obviously, but he does lack confidence a little physiacally (though has improved a lot) and I don't know how gentle she'd be and how much comparing him to others in the class there would be. Most of all, I really don't like being told that this is happening.
AIBU to tell her no?