Turn it around and think of it this way -- if your sons were still young and wanted to go to camp, on a field trip, church retreat, visit grandma, etc.... you would let them, wouldn't you? Now your little Yorkie wants a 3 day stay-over with your sons -- who you trust and know that they love her. Don't be mean, don't be selfish, let your baby go for a visit.
And....since she is going for a visit, you need something to do to fill your time while you miss her. Why not go on a cruise with your friends? What better way to console yourself whle your baby (don't think you mentioned her name) is having a ball visiting the brother?!?!!!!
Seriously -- it would probably be great for both of you!