Re: Teenage daughter.
I don’t have any kids but I remember very clearly what it was like to be a teen. Anyway, yes, I understand that your objection to her having boys at a party where it’s just her and her friends is purely due to the potential community gossip. Having said that….why not allow your daughter to decide what type of party she wants? There many be things which you are not willing to negotiate at all. Your answer should be a firm “no” to those requests. But things like this where is really is a bit of flexibility….open it up for discussion.
My 2 cents is that BEFORE your daughter brings it up again on her own (since you laughed it off last time she asked)….you & wifey have a private chat where you two agree on this….and then let you daughter know ahead of time that she can either (1) Have a party with her female friends only; or (2) Have a family party where she is allowed to invite boys. Its HER choice. Right now your daughter probably feels like she has 0 control and no matter what she asks, the answer is “no”. At least with certain situations, I think it would be beneficial to give her options and let HER choose what she would prefer (ie. showing her that you & wifey are not inflexible & are open to giving her what she wants under certain conditions). I totally understand you wanting to protect her b/c she’s young….but she also needs to learn to make choices/compromises etc. I think situations like this would be a great teaching tool which forces her to think about/decide what really matters to her when it comes to her “social wants” and what she’s willing to compromise to get it.
BTW, would you allow her to attend a bday party where boys are invited (and it’s not a “family” party)? I ask b/c if she has non-Muslim/non-desi friends…..this is what’s coming next. 
As for the sleepover, I’m once again not sure what you’re afraid of. Is it the community gossip? She’s 14…not 4. I completely understand not allowing her to spend the night at a house where there are other teenage boys (ie. if her friend has a brother). But if the ONLY man in the house is the friend’s father….and she’s sharing a room with her friend for the night with the mother inside the house….do you truly believe this puts her in a position to be sexually assaulted/raped? Will it make a difference if the sleepover is with a group of girls (as opposed to just 1 friend & her) in a house where the ONLY man is the father?