The Pie Dome or dw stadium is a short train ride from St Helens in fact from the george you can see the St Helens Train station the coach from the george will be cheaper than the train The saints shop won't be open sunday. We regard wiganers as inbred halfwitts and refer to them as pie eaters Here the number for the george 01744 753379
Which is ironic considering what the rest of the North West thinks of St Helens...
Sounds like you boys are gonna have a lot of fun. Tickets for Liverpool should be easy enough, for the Wigan game go through Wigan, they rarely sell out. The rugby at Widnes may be tricky for you (mainly due to the rivalry and ground size). But good luck.
You wouldn't get the bus from Manc to Sts to go back to Wigan, a bit silly. If i was going to all those places i'd hire a vehicle of some sort.
You all should of booked into Warrington. Direct train to Widnes, Wigan, Liverpool and Manchester. In fact if you look on a map, its actually in the middle of all them places.