Who makes the wedding decisions. Parents or bride and groom?

My 28 year old daughter has asked us to pay for her wedding to her live in fiance'. We have always been cordial to him, but he is not a "family guy" and doesn't wish to become part of our family in that way. He avoids family situations. We are willing to give our daughter a nice wedding and reception within our means. He constantly pushes for more. We are also not into drinking. Our own friends attending, who know our daughter would be offended and it would give them the wrong impression about us. . My daughter, in an attempt to manipulate us said "fine, we'll just pay for our own wedding." I replied that I am sorry we can't agree, but if they choose to do this, we will understand. At least it won't be perceived that we are paying for the liquor, and we will be there either way. When this didn't work, she called us back and asked us again to pay for the wedding. We are back to square one. Should the parents who pay have no say in these things. Their argument is it's "their wedding" and we should do what they want. My argument is if we are paying and hosting we should at least have the right of refusal on certain things. We are not trying to control everything. She is having everything else she wants, not to mention that we cannot afford the liquor bill.