You’re right, your DH is wrong.
In his head he’s imagining the beautiful beaches of Europe, when you’re on holiday and you walk out of your hotel and on to a lovely white sandy beach, no hassle. The reality in this country is you sit in a traffic jam for hours on end, even to get to a shingle beach. It’s windy so you get sand in your food, the sand is dirty, there are ALWAYS sticks poking out of it. The sea is grey.
I live near the sea. I have 3 separate beaches within half an hour drive. It’s brilliant. One of them has some sand too 
As a child, we visited a lot. Would hop on the bus (saves sitting in traffic) and spend the entire day at the beach. Of course, we’d soon get bored of just sitting there (could never swim, too effing cold) so we’d go off and play on the green, we’d go to the amusement arcade or play crazy golf or go to the funfair. It was BRILLIANT. And wha’dyaknow? It was a shingle beach.
I think just being near the sea, being able to go on walks on a crisp winter’s day and take a great big sniff of sea air is just fantastic. Beaches are more than just about sand. Children don’t give a shit about sand over shingle. They’re just at the beach.
I really wouldn’t look at Bournemouth or anywhere seaside-y to be honest. The areas get stupidly busy during peak season (when you want to go to the beach) and are dead out of season. Plus, the main roads around Bournemouth (and The Witterings if you go the other way) get horrendously busy in summer and can make you feel trapped. Live in a town/village near a beach but also near a city. You want half an hour drive to both (max). I know that narrows down the search a bit but it’s madness to move to an area with no prospects for your children just to be close to a sandy beach.
You need to weigh up what’s really, really important to you. Is it to be close to friends and family for the support network and to spend more time with them? Or is it to be near some sand? Do you want good transport links to London? Where are the good schools? Can you chat to your friends and family about the areas around them? Visit for more than a few hours? What about hiring a cottage or something in the area you want to live for a week at some point? It might give you a good idea of what the area is like to live in rather than just visiting for a few hours and you can see how it works for you.