My boyfriend is been so nice to my kids but how do i know if he is ready to have me and my kids?

me and my boyfrind live together with y two kids as of 2 days ago and he works 13 hours days monday through wendseday and my kids are sick right now so he hasn'rt been getting alot of sleep how can i make sure that we are gong to be okay and still las is there anything that i can do to make sure he gets enough sleep so we don't fight