Ultimately, you're in the right. If you don't feel comfortable with her having that party without you guys, then that is up to you. Even if you're wife was comfortable with the party, I would think she would still support your position. You & your wife are a team. That's something my wife & I are still working on 16 years into our marriage. Making sure we communicate our feelings, & working together toward solutions. While I might've allowed a child of mine(I don't have kids, we don't want any) have a party in those circumstances, it would seem to me, that erring on the side of caution is a better solution for compromise, rather than going with your wife's opinion. I'm sure you don't want to be a helicopter parent, but, at the same time, you love your child & want to(rightfully so) protect her. Infact, that's your duty as parents is to raise a child & make decisions on how a child is raised. I'm not a believer in free range children personally, it just makes sense that you want to guide your child to a secure future in general. Everything you say your child can, or cannot do, is something that they take in & can learn from. Every experience we have in life, everything we taste, touch, smell, etc. trains & molds us into who we are as a person. I would like for your daughter to appreciate that you're trying as a father, to protect her, & that you care about her safety.
In general, it sounds like you need a nice, calm, relaxed family meeting. Try to make the atmosphere as relaxed as possible, don't give the feeling that you're pissed off or anything. Don't raise your voice, even if the rest of the family does. Normally, people who are shouting at someone who is calm, will eventually cool down. Try to calmly explain your feelings with your family, & point out how important they are to you. Emphasize to your wife, that you & her are a team. There may be times when you'll go with your wife's opinion, but she of coarse needs to be willing to do the same.