Hi Ed,
I work in Rotterdam, commuting by car via Calais and know the area of Western Belgium and Southern Holland (below Amsterdam) really quite well.
First of all, most Dutch and Northern Belgian people speak a reasonable standard of English, and so you shouldn't have any problems.
I'd suggest you do some serious investigation of the possible ferry crossings - Dover to Calais or Dunkerque will be the lowest price and fast, which might be best for the dogs - Harwich to Rotterdam or Hull to Europoort (Rotterdam) are much longer crossings, but will save you a fair bit of driving.
Questions: What do you like doing? Cities? sights? shopping? food and drink? historic places? battlefield history? birding or wildlife?
Belgium:
Camping Blaarmeersen on the outskirts of Gent is one of the best campsites in Belgium - great for Gent city centre, and also Brugge - both are gems. Beer and food in Belgium is fantastic too
South Holland:
South of Rotterdam the coastal dunes run along the mouth of the "Rhine" river for 30+ miles - great camp-sites, some quiet and secluded, some near holiday towns like Renesse
Immediately North of Rotterdam are the Dutch Golden Age towns of Delft, Den Haag, Leiden, Utrecht, and Amsterdam. A good starting point is the Delft camp-site Delftsehout, good quality, in the grounds of a large park, and a 10 minute walk to the city centre and the excellent Dutch railway network with direct links towns.
Robert