Look at the train timetable site
http://ojp.nationalra.../en/s/timetable/times
I can't advise about times and fares as you don't say when you are planning to travel. It looks as if you have to change once, in Chester - you're looking at a journey time of about 2.5 hours. If you decide on a train (no obligation at that stage) then you can click the Fares button at the bottom of the page which tells you all the options, cheap times for travel, etc.
Does your mother have a senior railcard? May be worth looking at, it costs something like £24 but saves up to a third off the fare (but not on all trains).
I hope this helps.