They will still love Paultons as there’s the next level up to explore now. We love the rides so I’m sure they will.
Crabbing at either Lymington Quay, Keyhaven Quay, or the crabbing bridge between milford and Keyhaven.
Ferry and or walk to Hurst Castle (round the island race this Saturday, so best viewing point to see all the yachts) then have a wander around milford - perhaps grab a pizza from the wood fired fire engine pizza at The Smugglers in Milford.
For a day at the beach try Friars Cliff. Walk along the cliff path to Highcliffe Castle then down to the beach in the zig zag and back along the beach.
The Beach Hut café at Friars Cliff does great seaside fayre or you can continue to Avon Beach on the promenade to The Noisy Lobster which does take away as well as sit down (check the menu for pricing & book if you fancy it). Then carry on to Mudeford - crabbing, foot ferry to Hengistbury Head and the luxury (£300k+) beach huts. The noddy train runs from there to the Hikers Café so you could walk or bike one way and catch the train back. There are “Boris” style bikes and sometimes an electric scooter there to hire as well. Beryl bikes I think they’re called.
In the New Forest, please enjoy the sight of the ponies, donkeys, cattle, deer etc but look and don’t touch or feed - they are all owned by commoners.
Good places to see them included Brockenhurst - grab a picnic lunch from the Bakehouse or bring your own and wander out to white moor where you’ll see lots out in the forest. Plenty of car parks, toilets, ice cream vans.
Where are you staying? Can give you more specific details perhaps.