My experience has been that younger kids usually have zero issues with it. Their world is about pretending and playing. So, the idea of feeling one way inside and looking different on the outside makes a lot of sense to them.
I have four kids, ages 12-4. The younger two needed very little explanation. The older two needed more. All four needed to be reassured that it doesn't change our relationship and that I'm not abandoning them. My 8 year old needed to know that this won't happen to him. The oldest needed to know that this doesn't affect him, and I won't embarrass him at school, etc.
Part of it really is generational though. People younger than 30 tend to be more accepting anyway.
I have noticed, though, that kids can take their cues from unaccepting parents. Kids tend to pick up their parent's biases and prejudices. In the case of a messy divorce, kids will usually pick a side. But that's true for non-trans related divorces as well.
My anecdotal experience (mine and quite a few trans friends I have with kids) is that kids are accepting when the relationship is good. Adult children are a bit of a wildcard. So I would suggest talking with your dad openly about it. Tell him it hurt you, because you suspect that he's using the kids as an excuse.
I wish you the best of luck. And please do keep us updated.