I would word it this way:
I just received the invitation to Child's party. We'd love to go, but first we need to know when it's scheduled, because DD has other commitments that day. Could you please let me know as soon as possible? Thanks!
IMO, I think it's not very nice to hide the time from the people you're inviting, simply because of the situation in your OP. It creates a bit of stress trying to figure out if you can even go. It may not be rude, but I wouldn't like a person who did that. I understand that hosts need everyone to respond ASAP, but some people, upon receiving such an invitation, would think, "Well, they didn't even bother to put the time on there? Okay, not gonna waste my time on that."