It's a tough age (my oldest is 6) for these kind of conversations. For the time being my daughters think that Daddy just has to sleep closer to work (and because he's in law enforcement - he's always worked crazy days and hours and they are used to it). But eventually - there will have to be a conversation (unless he shakes off the fog) - and I fully intend that he will be the one doing the explaining.
I'm sure your daughter asks your H these questions, but this actually seems like a completely reasonable conversation to have with your H as well. You can do a temperature check and ask how D seems to be handling the situation when she is with him and share that she seems distressed when she is with you - and share how you have handled it so she gets a consistent message from both of you. Perhaps your ICs would have some suggestions as well.
