I don't have much good advice on getting your baby to drink - when we were having issues getting my daughter to take in anything (at all) during a trip last year, we tried everything including spooning in milk and water, and 'injecting' some with a medical syringe. Eventually she started using the sippy cup, but, it was tense for a while there.
As for checking for a wet diaper - you could put a diaper liner in your baby's diaper (a cloth or paper one that would feel wet even if the disposable absorbed a lot), or you could use cotton diapers for a while, because those don't absorb so much. Or, you could put on 'big girl pants' under the diaper - again, same principal - the cloth will feel wet even if most of the liquid is soaked up.