Southeast England shortbreaks for 1 and 3 year old?

It really depends on where in the Southeast you are thinking about. The New Forest has wonderful scenery and access to the coast. Kent has some amazing National Trust properties, some of which have properties on site. It also has beautiful scenery and coastlines.

Littlehampton has the sea (obviously), sandy beach, Harbour Park
www.harbourpark.com/opening-times/
And a short ride away Flying Fortress soft play
flying-fortress.co.uk/
And Out Of Bounds
out-of-bounds.co.uk/
Nearby Worthing has a pier, lots of eating places and shops.
There are plenty of cottages and Airbnb in the area, and Chichester is a very pleasant day out

We haven’t been but I’ve heard good things about Sandy Balls in the New Forest.

www.awayresorts.co.uk/parks/hampshire/sandy-balls/

There are two wildlife parks in the Kent - Port Lympne and Howletts

For a few days with young children and grandparents I would not travel too far from where you live.
Wherever you go you will find things to do. I think it’s a lovely idea and hope you all enjoy yourselves. The seaside is a good choice especially if weather is ok. Kent Sussex Hampshire Essex, you have so much choice.