We will have a car rental for our Highlands portion of our trip. I originally was planning to leave the car in Glasgow and train to Chester (or Conwy depending on when we leave Glasgow). Then train from Chester to Conwy and Mount Snowdon. After this we will be making our way to Manchester to fly home. It seems with a car might be easier to explore Conway and Mount Snowdon. Would you agree? So how's the drive from Glasgow to Chester or Conwy? The cost difference is only the gas. The price of train tickets vs the extra days of rental are even.
North Wales is easier with a car, particularly Snowdon.
Glasgow to Chester or Conwy is straight forward, being motorway nearly all the way. The M6 is a nice ride around Shap and the Lake District. The Preston to Chester section is more tedious. It will take about 90 minutes longer driving than taking the train, but you could stop in Kendal to break the journey.
I would get the train to Chester and then pick up a car from there.
The journey from Glasgow is very straightforward on the train with just 1 change at either Crewe or Warrington Bank Quay. Chester is a nice place to stop and visit in its own right.
We drove all over Wales; it is great just to drive up to all the Castles. Be sure to get your CAWD Explorer Pass for 3 or 7 days. Taking the train from Glasgow to Chester is a great idea if you want to speed up your trip to allow more time in Wales. Chester was originally a Roman Fort for XX Regiment and has a Wall that you can walk around the town and great "Tudor" shopping district. You could rent a car in Chester and return it to Manchester. We had no trouble driving everywhere; except we did have to stop for sheep!
You might find the rail fare to be cheaper if you pre-book (ideally 11 weeks out when the cheaper fares get loaded) a ticket from Glasgow to Warrington Bank Quay and then buy another ticket from there to Chester (well worth a visit) or Llandudno Junction to then hire a car again. This may work out cheaper than one through ticket. www.nationalrail.co.uk
You may wish to visit the Lake District (NW England) instead of NW Wales as that will mean you cover less distance and is more convenient when coming down from Scotland.