I absolutely and TOTALLY get why this would upset you.
People up thread who are saying "Meh, it's just a haircut" really don't get it.
I think if your Ex had taken DS to a barbers and your DS had actually wanted a haircut, well, I don't think you would have minded at all.
It's the fact that the OW not only has her claws in your DH (yes, yes, he is at fault too), but now she has extended her claws to your children. She's done something that your DS didn't want. And you have been powerless to stop it, as you weren't there.
That would really get to me, in an almost gutteral way, I think. She is stepping on your territory and I bet you wish she'd just fuck off and die. Sounds harsh, but you're allowed to be angry.
You are only 11 months post split, and I want you to know, that this WILL get easier with time.
My first "D"H cheated on me (many times) and I left him. After 20 years, his whole family cut me off, they literally never spoke to me again. Despite them knowing that he was the cheat. Their reasoning? He was just having a bit of fun, whereas I was splitting up a family.
Can you imagine how angry I felt? But I still had to smile sweetly and wave the kids off on holidays with all of them. It was hard.
But time is a great healer, it really is although I still wouldn't piss on any of them if they were on fire You just learn to feel indifferent.
I have rebuilt my life now and have a lovely DH. Four of my close friends have also been cheated on and left....and every single one of them found love again and married again.
In 8 years time, your DS will be an adult and you will no doubt married to someone else, who you will adore, and you will be so thankful that you saw your ExH true colours.
Also, fwiw, your Ex and this OW are both capable of cheating. I used to say (about my Exes girlfriend that came after me) that I was sure he would cheat on her, because, let's face it, if you can cheat on your wife of 20 years, who is the mother of your children, I'm sure you can cheat on a woman you aren't even married to. Guess what? I was right. By the time that poor woman left him, she was an absolute wreck.
Your Ex and OW won't last, they really won't. Because they are of the cheating variety. They are capable of cheating. They are capable of lying. They are capable of these things, and here's the kicker, they both know what the other is capable of. Their "relationship" will be full of insecurities, because they both know what the other is capable of.
Build yourself a new life. Start dating. And when it all goes tits up, ou can watch it from the sidelines, pour yourself a vino and have a little chuckle.
You are worth more than these cheating arseholes. Onwards and upwards....