Boyfriend taking baby!

Out baby is 3 weeks old and my boyfriend wants to take her to his house for an hour or two with out me. What would you do? is that okay? He also wants to watch her during my baby shower( had baby before shower so we are having it now) because she is not going to be there due to it being cold season. i trust him with her fully i just don't know if it's an acceptable thing to do. we are also teenagers, and my parents always try to step in and be parents to my daughter. when i mention him taking her without me they get super upset and say no.