Cape Cod Bay and the kettle ponds around Cape Cod are all milder and warmer, if you want to avoid the Atlantic and the waves. The tide in the Bay goes out for miles. There should definitely be some public beaches for the Bay, but you might need to get a local beach sticker for your car to access the ponds. I'm not quite sure how to go about doing that because I've always just borrowed family cars.
That said, the Atlantic off CC is still warmer than the North Sea. It is swimmable in July and August. If you do want to brave the waves, Coast Guard Beach on the National Seashore is the one I'd take the kids to. It's slightly less rough than Nauset, there is a good lifeguard presence there in summer, and conditions are generally suitable for boogie boarding, skim boarding and sometimes surfing. You can literally spend the whole day there. The only hitch is you will need to park about 1/4 mile away from the beach and then haul your beach stuff with you onto a little electric shuttle bus. Everyone does this, though, so it's not like you'd look ridiculous - when I was a kid, my family managed CG Beach and the shuttle bus several times a summer with something like three adults and eight kids of varying ages, plus our boogie boards, towels, chairs, coolers full of food, baby tent, etc.
Rent a car. You will need one. There is very little public transport on the Cape, unless you decide to go no further than Hyannis. There is a train service running between Boston and Hyannis starting this summer, which might be handy for you - I think tickets are about $30, but it's meant to be a leisurely ride with a dining car and will hopefully bypass some of the worst traffic. The MBTA website should have more info about it.
Traffic can get very bad on the Cape - there are only two bridges over the canal and only one two-lane (most of the time) highway. If you head from off-Cape towards the canal after 9 am in the summertime, you will sit in traffic for hours. Literally hours. I am not kidding. Try to plan accordingly and ask the locals for advice about when to go - most should be happy to help.
Word of warning about renting a cottage: it can get very expensive to stay on the Cape. That doesn't mean you won't find something affordable, but it does mean that you might have to lower your expectations, depending on what they are in the first place. My SIL and BIL were very, very disappointed in their cottage rental when they came to visit last year. Their house had exterior paint peeling round the back, the decor was badly in need of an update, and there were spiders all over the place. SIL and BIL are very houseproud and kind of expect immaculate, spider-free places wherever they go. If you are also into immaculate, modern decor and granite counter tops in the kitchen, I would suggest renting from a resort like Ocean Edge rather than from a private landlord, who could very likely be an elderly person using his/her older house to supplement Social Security income.
I would also vote in favor of Plimoth Plantation. Plymouth itself is a nice town - there's also history with the Mayflower II replica, Plymouth Rock, Coles Hill cemetery, and it has a bit of a nightlife on the waterfront. If you are into living museums, there is also Heritage Museum and Gardens in Sandwich.
Grew up just off Cape Cod with relatives on Cape, and worked in Plymouth for a year before moving to Scotland. 