"My daughter is 3 1/2 and I am having some problems with her. She goes to her great grandmother's during the day and she likes to run around with no clothes on. This really bothers my grandmother in law. I don't know how to get her to want to wear her clothes. She has also recently started getting dressed with no underwear on. And she touches herself down there. What do i do to stop this behavior..or is it normal?"
The only problem I really see is the conflict of interest that your GIL wants her to wear clothes and she doesn't want to. Your daughter is old enough at 3 1/2 to understand that she has to respect her great-grandmother in general, and to follow her rules in her house. So sit down and have a talk with her about how she is allowed to choose what she wears (although she has to wear underwear if you want her to), but there is no choice about wearing clothes at great-grandma's house, she just has to do it. If she doesn't wear clothes there she doesn't get to go. This is going to be the first of many conversations about appropriate attire ("no shirt, no shoes, no service" is a hot topic in our house this summer), and is part of the process of learning to balance her own desires with the social compact.
There's no point in trying to make her want to wear clothes. You can't make her want to do anything, and it doesn't matter if she wants to or not, as long as she follows the rules. This is an important distinction that she's probably too young to even begin to understand, but that will become really important to her when she's a teenager and has to do all kinds of stuff she doesn't want to do. I mean, who actually wants to write an essay on Beowulf? But she'll have to do it anyway, even as she maintains the integrity of her own feelings about liking it or not liking it. (Talk about framing narratives--how much do you not want to have to deal with your daughter's nakedness, but you do it anyway because sometimes you just have to do annoying things as part of life.)
To ease the pain of having to wear
the shackles of the patriarchy clothes at her great-grandmother's house, you might want to institute an official Naked Time every night between dinner and bedtime. Naked Time is a popular event in my house, and I'm guessing there are a lot of readers who are laughing because their kids love Naked Time, too.
The touching herself is completely normal and really healthy. You want her to know her own body and to know what gives her pleasure. It's only going to help her maintain self-confidence as she grows older and starts to becomes more self-aware, and then later when she starts dating. But she shouldn't be doing it out where everyone can see, so tell her it's one of those things you do by yourself with no one else around, like pooping or picking your nose. If she does it in front of other people again just calmly and non-punitively send her to do it in her own room.
She sounds absolutely normal and right on track developmentally. The whole naked-love thing is both disconcerting and hilarious, but it seems to go on for months (if not years), so just establish some boundaries and then try not to worry about it.