I can understand why you're upset, but I think you need to take a deep breath here and try to see the bigger picture. I can't believe this was a malicious act by your MIL done deliberately to upset you; she was probably just meaning to be helpful or responded to something one of your kids said. She may not have realised it was your youngest's first haircut or the huge significance of that to you.
It is really important not to let something like this destroy your relationship with your in-laws. You mention upcoming holidays but there will be numerous other times your husband will want you all to spend time with his parents too - and if you don't or you resent it, this will put pressure on your marriage. Your in-laws are prepared to look after your kids - that's actually a good thing and you may be very grateful for that in the future, however you feel now.
I lost my mum unexpectedly when my kids were little and my dad proved useless at any practical help, so I have been indebted to my parents in law for providing help with my kids, both planned and in emergency circumstances. My mother in law has a different approach to me (huge amounts of sweet treats) and has sometimes got it horribly wrong (notably once letting my kids open their Xmas stockings without me there, which I had bought and wrapped!), but I have realised it all comes from a place of love and she means well. It doesn't have to be a competition between us for control (I'm the outright winner there for 99% of the time just by being the mum) and the kids benefit enormously by having interested and involved grandparents.
So please don't let yourself be poisoned against her forever over what was probably a misunderstanding and something that may possibly feel quite insignificant later on, hundreds of haircuts later. It really isn't worth it, in my view. See if you can forgive her and move on, for the sake of peace all round, not least your own.