Welcome to BetterBidding!
Happy to help and i'm local to the NYC area, so you're in good hands.
As you point out, with HOTWIRE you can search for up to quad occupancy and hotwire guarantees that the room will accommodate the number of guests you included in your search.
All Priceline reservations are for double occupancy, after that it's at the discretion of the hotel (although in NYC, where rooms are often smaller than most other parts of the country and hotels have a high percentage of rooms with only one bed it's considered fairly risky to book for double occupancy and who up with four guests). The one caveat to this would be PRICELINE EXPRESS if you can find a hotel that offers a BED CHOICE option and one of those options is designed to accommodate the number of guests in your group. Note that technically your reservation is still only for double occupancy, although i don't know of anyone who has yet had an issue showing up with 3/4 guests when they booked a specific room type and that room is designed to accommodate the number of guests in the party.
Personally i would be fine booking for double occupancy and showing up with 3/4 if the specific room type i booked was designed to accommodate that number of guests, but you have to do what is within your own (and your in-law's) comfort level. If a concern, you could further minimize any potential issues (although as per above i think think the chances of a problem are minimal) by having two guests go to check-in while the other two grab coffee at a nearby Starbucks, bodega, etc.
While i don't think your budget is going to be an issue (i'm already seeing things like the Westin Times Square, Omin Berkshire, Warwick New York) i would ask if you really need a 4.5* property... or would you consider a 4 star that had good reviews? As an example, i'm often an advocate of the Crowne Plaza HY36 Midtown Manhattan.... fairly new hotel, gets great reviews, and extremely centrally located; for your dates not much savings vs. some 4.5*, but at least knowing your thoughts about something similar to this, although only 4 star rated, would give us a sense of what to recommend.
Let us know if a well reviewed 4 star hotel is also on the table as a possibility, as well as your thoughts if booking PRICELINE EXPRESS (w/ Bed Choice) is an option, and we'll take it from there to suggest your best options.
Please remember to return to BetterBidding and use the PRICELINE and HOTWIRE links on the board to begin your travel purchases... or thru our sister site MAPSandHOTELS.com for your regular rate purchases.