As my profile name suggests, I am also from Norfolk... and it's an amazing place all year round, but especially in summer. I'm definitely biased towards North Norfolk where the best beaches are, and where i'm lucky to be from. Agree with what everyone has said above. Bewilderwood is great. Holkham has a big adventure playground with high ropes course, plus bike hire and the hall to tour. Last summer they also had Feastival running each weekend with lots of food stands, music etc, such a great atmosphere which I expect they will try and repeat. and then across the road is the enormous beach and pine woods. They're also setting up the brand new Camp Elwood which looks great, so take a look.
Brancaster beach is brilliant, but yes, parking was an issue on any particularly sunny day this summer. The access road is subject to tidal flooding so if you go, check this first. Pinewoods in Wells has a pretty big car park and is stunning.
You can visit the seals at Blakeney/Morston. Sandringham House & gardens, plus the woods there. A friend set up Brancaster Boards last summer and runs paddle boarding trips. Houghton's gardens are amazing and they often have big exhibitions, last year it was Anish Kapoor. Wells to Walsingham light railway is an experience... Hunstanton has crazy golf etc. www.visitnorthnorfolk.com
So many great pubs along the coast - Jolly Sailors with huge beer garden and great pizzas. White Horse with amazing views of the marshes, and their new Marsh Bar marquee. Most pubs are child and dog friendly.
For holiday cottages definitely check Barefoot Retreats. Also www.norfolkhideaways.co.uk
. Lots are rented privately, and use sites like http://www.brancasterstaithe.co.uk/
Coastal properties book up really fast, with many people doing repeat bookings. Inland the prices are a bit more reasonable - have a look at Docking, North & South Creake, Binham, hindringham, Melton Constable - all within easy drive of the coast.
Have fun planning and I hope you have an amazing holiday.