I am a custodial step-parent and have been for the last 10 years. I have always signed papers. I do not sign binding documents that only a parent should sign (medical releases). I do not know the laws on that, but it was just something I felt their father should sign. I have attended parent conferences, etc, but that is because the girls have always lived with my husband and myself. We have just always made copies of the report cards for their mother and always made her aware of what was going on at school. When we were in a car accident, I did sign all the hospital paperwork. The girls are on my insurance for dental and my husband's medical. I am considered a legal representative of the girls as my husband's wife.
As for haircuts and such, we have always been the one to pay for the cuts so we have taken the girls. Their mother has not had a problem with this. If she is preventing you from cutting her hair, then she needs to be responsible and take her for the cut and pay for it.
When the girls were old enough to shave, I spoke to the mother and asked her if she wanted to be the one to do this for the first time with her daughters. She opted to do this with the older one, but the second one she said it was fine for me to help her.
I don't know if this helps, but I wanted to share my experience.