What kind of rights do step parents have?

ok this question is two fold the first half is a bit complex my ex and i split up after some domestic violence with out getting into to much detail my twins were less than a year old the judge recommended supervised visitation every other weekend no over night visits yada yada..any how he visited the kids under the supervision of his mother for about two months before i found out she was never supervising st the time i couldn't afford a lawyer and didn't think i could do any thing with out one a little back ground on my ex is that he never actively participated in parenting he never acted interested in them or me for that matter that's beside the point by the third month we worked out an unofficial agreement that he could see the kids when ever he wished making his visits almost nonexistent any time he did see the kids for my own comfort i stuck around he remarried later and from what i saw she was fairly decent to the kids so i figured she was an appropriate person to keep an eye on him and the kids shortly after i started leaving the kids with them he started venting to me about how his new wife was pushing him to go for full custody knowing him well enough to know he doesn't have much interest in the kids i didn't think much of it as time went on she got more pushy about it and has decided that she doesn't like me in attempts to make me mad she dyed my daughters hair pink my twins as of now are four years old my daughter has medical problems and we visit children's hospitals out of state monthly at least and in my personal view i think it make a parent look irresponsible to dye such a young child's hair so i took her home tried to wash it out some came out but most of it stayed in and left blotchy blond orange and pink spots in her hair i tried to strip the color with hair stripper and it just wouldn't come out as i was rinsing it i found that her hair being so fine and baby hair started to fall out i was left with no choice but to shave her beautiful hair i was furious and when i took the kids to his house again his wife told her that i was a bad mother for shaving her head and that i had lied to her my daughter told me when i picked her up amanda says my mother is a liar she sounded so angry and hurt i brought it up to my ex and it cause a fight between him and his wife and three months before their first anniversary she moved out needless to say im relieved but now he has started talking about trying to work out their differences im worried about the things she will say to my kids especially about the fight she has told all of her friends and family that im the reason her marriage failed what will she tell my kids my idea is to tell him i don't want her influencing my kids and ask him to visit the kids in my home can i do that? and what are my rights as far as her bad mouthing me to my kids? the other part of my question is that im too have plans on remarrying again and would like to know my rights as a step parent can i pick my step child up from school can i take her to doctor appointments and attend parent teacher conferences also with taking my daughter to doctor appointments out of state will i be allowed to take my step daughter with me i like to take two kids so the trip can be more fun and we also visit the attractions and i would like to involve her in the fun we will make family trips but a trip with just three of us is special in its own right