I think that the simple answer to your question is 'No'.
I've just worked my way through all of the holiday parks identified by the area's official accommodation finder, here:
http://www.ntb.org.uk/index.cfm?fuseaction=sea rch.accommodation&categoryid=82
None of the sites seem to fully match your requirements. I've got a suggestion, however, which might be of interest to you:
Park Resorts have two holiday parks, just 3 miles apart, either side of Newbiggin-by-the-Sea. One of them is Church Point which offers absolutely nothing other than accommodation and scenic views. (i.e. apart from the static caravans, there are no facilities on the site). It's not actually designated as 'adults only' but, due to the lack of facilities, it's unlikely to be packed with young families.
People staying at Church Point are allowed to use the facilities (including the indoor pool) at the much busier Sandy Bay park (which, as I've indicated is a 3-mile drive away). So, unfortunately, you won't be able to avoid the kids splashing around in the pool but at least you shouldn't have them disturbing you around your caravan
http://www.park-resorts.com/park_info.asp?Type =&ParkID=36
Chris