I grew up in Southampton. The train station is easily reachable from the port and you can get a train to Winchester. Winchester is very beautiful and Jane Austen lived there. Very old and you can visit Jane Austen's grave in the Cathedral. The Catherdral is beautiful. Most importantly for your mum, Winchester is more or less FLAT. Bath is on a hill. Big hill.
Make sure to book for a lovely pub lunch in Winchester.