Of course you can bring your kids. We understand that they're an important part of everyone's lives.
If your invitation says “and Guest,” then yes, if not, we would prefer if it was just you.
You absolutely can! The discount code is only good for the 22nd-24th, so you just need to make a second reservation for whenever you'd like to stay additionally (side note: this would be at the normal rates and discounts for the hotel, and another hotel might be cheaper).