Valet parking is under the hotel. However, there is a garage right across the street. During the week, use either for similar price. On the weekends, the garage across the street is much cheaper and very easy to access.

lots of kids but with parents

So glad that they were able to answer your question. I drove, therefore did not use shuttle.

Just valet. You won't save much if anything by self-parking because street parking is almost non-existent so you'll have to pay anyway. And the commercial garages are not in-and-out so unless you let the car just sit you will actually pay more.

Your questions can easily be answered by the hotel. Give them a call