Cottages near the beach, scenic, accessible, luxurious and affordable, I highly suggest that you check out the wide variety of choices from http://www.bluechipholidays.co.uk. They have plenty of cottages all over South West of England that you can choose from. They are also near parks, and definitely, your kids would love to stay near parks for a fun stroll right? Here's also 5 great spots that is worth checking out with your family: http://englishmum.com/five-great-spots-for-uk-wildlife-holidays-with-kids.html
Can highly recommend here. We've stayed at a few of the cottages and all are absolutely lovely. We visit Dartmouth and Kingsbridge when we're down there so they're not far away - 15 miles or so. Although maybe too far for you.