How about a trip to the teddy bear museum with the young children with the Easter holidays in April. This site has details about the museum.
Occasionally there are direct trains from Sway to Dorchester but usually it will require a change at Brockenhurst, New Milton or Bournemouth. Train times can be found here.
Cross the footbridge at Dorchester South station and leave the station from platform 1. Follow the route on the map below. The walk will take about 20 minutes, maybe a bit longer with small children.
The route takes you through the town centre and gives the opportunity to stop for refreshments on the way there or on the way back.
