I'm with Daycarewhisperer on sleep times, personally I wouldn't push the sippy cup until you get him on a good routine, too much change at once can be to much for one so young. His bottle sounds like his naptime soother to me.

I had a baby once who always took a bottle for nap even after lunch, sometimes she only drank a few sips then fell asleep.

Maybe talk to Mom about possibly replacing the bottle with a soother? Could help, bottom line be very upfront with the parents you all need to be 100% on the same page in order to ensure success.

Welcome and good luck.