Hmm... it isn't rude, IMO. I'm actually more concerned with whether the kid will be willing to stay with you for a few days without her parents, considering she's only three? I say this because I've two nieces (aged 4 & 10) who are very close to me and will go places with me but will not spend the night with me. Come bed time, they always want their parents (or their familiar beds). My 4yo niece may even cry and that can be a real headache.