OK, I think I'm getting it. You don't live with your MIL. You live with your mother. Your MIL wants money from your fiance and accepts gifts from her daughter. (I assume, your fiance's sister.) So far, is that right? You judge that she has plenty of money, and are annoyed that she is not buying anything for your baby.
Also annoying to you is that she gets money from your fiance. And, there is this fight about Dreft. You bought some Dreft, and she has asked you for some of it, to wash sheets and blankets that she will have at her house.
SO .... let's look at this.
First of all, it is really an exercise in futility to judge someone else financially. You don't know what demands she has on her money, and you are going down a slippery slope if you try to judge this. There is nothing wrong with saying to your fiance that he should not be giving her money, but you may as well shout at the wind. If she asks him, he will probably give her some. Even if she is wasting her money by your standards.
Regarding providing her some Dreft -- are the sheets and blankets for the use of the baby? If so, give her a box of Dreft for Christmas and stop fighting about it. If not, forget it, she can buy her own detergent.
She lives with her mum and her mother in law is asking for stuff.
I'm getting kind of lost -- when you say things like "I live with my mom, and she wants" it sounds like your mom wants.
Your mom wants to wash the sheets and blankets?
I live with my mom and she wants to wash the sheets and blankets her daughter bought for her house with the soap I bought.
You are living in her house? And she wants to wash sheets for the baby but wants to use your Dreft? Or do you live somewhere else and she wants to set up a baby bed in her house and wash the sheets for it?