I could never persuade dd to drink very much from a sippy and have ended up resorting to a normal cup for everything and a bottle for milk. For us it was the only way. At 10.5 months you could cut back to 3 feeds a day, but milk still should be his main source of calories for the next 6 weeks or so, not that something magic happens in 6 weeks, but it's better to err on the side of caution!
As far as the weight gain goes, I wouldn't worry too much - he probably got a whole lot more active, it's ok as long as he doesn't actually loose any. Keep an eye more on the diapers.
I think your first step is to experiment a bit with the milk source, another brand of sippy, cup... and be assured that in my experience babies behave almost always WAY better when mummy isn't around than when she is, don't cancell your vacation just yet!