How to convince my Mom to let me stay in town for a party?

Ok well my bday was about 2 weeks ago and I had a small party with my family and two of my closest friends. My mom had to beg my friend, rose’s, mom so that she wud let her come and she did. Now rose’s bday s coming up, its next week. I was suppsed to go to Las Vegas with my family this weekend but my dad got sick and had to be in the hopsital. Now hes out and we decided to postpone our trip for next weekend but the thing is that Rose invited me to go with her and some other friends and family to six flags for her bday. I asked my mom if I could go but she said that if we go to vegas then I cant go because I have to be with my family. But we go to vegas practically every month to visit my brother and rose’s bday is only once a year and her brother is willing to pay for all of us. I think that it would be really messed up if I didnt go since she came to my bday party. Rose told me that if my family goes to vegas that I can stay wit her at her house for the weekend because she really wants me to go to six flags with her. How can I convince my mom to let me stay because I know that family is important but friends are also important to me. I mean, cmon, rose came to my bday party and its not like if we dont go to vegas very often.