Uhhhhh.... I hate to say this, but it's only the beginning. OP tend to want to get on children's "good side" and play mom or dad so the person they are dating will see what a great mom or dad they would make. Unfortunately, this is something one should expect...
My suggestion is that you calmly tell H that you would like to be informed of any hair cuts, body piercings, tatoos etc... prior to them being done. You are her parent and have a right to be involved in decisions of this nature. If OW wants to pick out clothes, buy toys, things like that. You are fine with those kinds of decisions (D can wear those clothes when she's with H and not at your home). But hair or body changes.... you have a right to be involved with that. Tell him (and OW) it's disrespectful for this to be done without your consultation and approval.
Tell H you will be happy to do the same. Tell him you won't allow men you are dating to make changes to daughter's hair as well without H's approval.
Be calm and together. Do not fly off the handle. You will just give OW and H fuel for saying what an unreasonable bit@h you are and how H did the right thing D you. Don't give them that satisfaction.
In fact, OW may know, or hear about how your H is regretful sometimes and missing you. She may have done this hair thing just to make you angry so she can say to your husband, "See what a bad temper she has!!! Why on earth are you missing this woman?"
There is no arriving, ever. It is all a continual becoming.
