My step daughters mother puts up vacation pictures on Facebook...?

So she wants to take the child but you say no
and now you think she shouldnt be able to post about her own life on her own facebook page?
anything else you want to dictate? when she goes to the bathroom?

She is free to lead her own life
and you are free to MYOB

So you and your husband are the ones not allowing the child to go on vacation with her bio mom, and then you try to control bio mom's social media activities too? LOL You are either very young and naïve if you think you have a right to do that, or you need to get some professional help with your mental health issues.

maybe you should block them on facebook so she cant see them

Why shouldn't she? You don't allow her to take the child on vacation with her, maybe you have good reason for that, however it is not as if the child is missing out because her mother refuses to take her or doesn't want her there, she is missing out because you don't allow her to go.

If the child is old enough to have a Facebook account then she is old enough for you to explain why you don't permit her to take these vacations with her own mother.

She has had to accept you saying no when she wanted to take her daughter on vacation so she should be free to enjoy it and share photos of it without feeling guilty, it's you that stops the child being a part of it so it is you that should explain to the child why she is missing out.

Not only do I think its ok, I think its appropriate for her mother to do so. She is not sharing these photos to make her daughter feel bad or to make you look mean for not allowing her to go, just merely sharing her life with her FB friends like anyone else. It would be one thing if her daughter was not invited to go, but since she is often included there is no malice involved. I think your disapproval is based upon having to answer for you and your husband's denial of permission for her to join and her anger at you because of it. Welcome to parenthood. They aren't going to be happy with you when you tell them no, even when you have a valid reason to say no.

I think the woman should post what she wants on Fb. LOTS more people than her daughter see her posts. You and the child's father are why the girl hasn't gone on the vacations. That does mean the woman should have to pretend the trips never happened.

A better question would be, why don't you and "dad" let the girl go on trips with her other family? How often does your family take trips that include the girl?

If anything, the girl's mom posting vacation pics is likely to cause the child to resent you and her dad, for not allowing her to go.