Short answer: The tramway is the answer — open-top trams every twenty minutes, hop-on hop-off day tickets, and a toddler who will happily ride it for an hour. The wetlands are free with wheelchair-accessible paths and the tram stops there. The beach is pebbles, which is harder work than sand.
Seaton Tramway runs narrow-gauge open-top trams up the Axe valley every twenty minutes, and for a small child it is the best value in east Devon. Day tickets are hop-on hop-off, so you are not committed to a single round trip — get off, look at something, get back on. Dogs are £2 each way.
Start at the Colyton end rather than Seaton. Parking is free there, there is a good café with proper scones, and you save the seafront parking charge. It is the single most useful piece of local knowledge about the tramway.
Free, with a £1 parking donation, wheelchair-accessible paths and bird hides. The tram stops here, which means you can arrive by tram with a toddler and not have to negotiate a car park at all. The hides are also shelters, which matters when the weather comes in off the Channel.
Seaton's beach is pebbles, not sand. Pebbles are hard work with a toddler — walking on them is unstable, there are no castles to build, and a buggy does not go on them at all. The esplanade above is flat and fine; the beach itself is a sit-down rather than a play.
Park free at Colyton, café and scones, tram down the valley, get off at the wetlands for the hides and the paths, tram on to Seaton, walk the flat esplanade, then tram back. Almost no driving and a toddler who has been on a tram four times.
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