I am not sure I would use priceline though. You do not know in advance which of the motels Priceline will assign to you from a given "zone". Also, you may be assigned one that is not close to an interstate exit and you might have to hunt for it after dark. Of course if you know the motel name in advance, you can get directions online. But, a Priceline room may not be sufficient for you and five kids. With that in mind, I would doubt even more trying Priceline given the circumstances of travel that you have.
I would make reservations at motels at which you think you might want to stop. I would not guarantee them but would ask for either a 4pm or 6pm hold, depending on the chain's policy.
Then, I would vary my driving pattern, taking into account the days that I am traveling, i.e. December 19 and 20. Since they could be busy days for travel, and I might encounter weather enroute, I would plan on stopping before dark. That increases your chances of finding an available motel.
If I wanted to travel longer, if the weather were not a problem, then I would have alternate motels already picked out in advance and reservations made in advance. They can always be cancelled enroute.
Finally, here is what
www.BiddingForTravel.com has to say about more than 3 people traveling and using Priceline:
"1. We are 3 or more people wanting to share one hotel room. How do we know if the hotel will allow this and that we will get a room with two beds? We want to be guaranteed a smoking/non-smoking room. We want a room with kitchen facilities.
You are only guaranteed a room with double occupancy, regardless of what type of rooms the hotel may offer. Any special requests must be made directly with the hotel once your bid has been accepted, but the hotel is not obligated in any way to accommodate the request. It is very important to note that there are some hotels that Priceline uses that offer only one bed in a room, especially when bidding 1* or 2*, but it has happened at all quality levels. This should be taken into account if you require more than one bed. As to smoking/non-smoking, a hotel will take a request but can offer no guarantees. There is no way to bid for a suite or for a room with kitchen facilities. Again, you are bidding for a room only."