As I said in the first post, we had planned on talking to my parents about the kid situation at dinner yesteday night. Well, I decided that before we went over there and started a fight that I would call my dad and give him a heads up (also I was hoping to get his take on the issue). It turns out that my father is the one insisting that my cousin's kids are invited and when I told him that we were not going to compromise on this instead of saying that he isn't paying he said he isn't coming. Before I could even explain our reasoning he hung up on me. Needless to say we did not go over for dinner. On a good note, my mom is still talking to me.
Bottom line is that we (FI and I) are bummed that we will most likely have to postpone the wedding but this will allow us to plan and pay for it ourselves so we can keep our sanity. Thanks for all your advice.