As said previously, if one rear wheel is a freewheel and the other a freehub with cassette, you can't do what you want to do and simply change the two. If so, buying a set of tools is a waste of money. The bike shop would tell you right off when you brought in the wheels that switching the two is or is not possible. You only need to look at both wheels yourself to see the difference at the lockring. The cassette has a flat plate making up the smallest gear while the freewheel is indented at this same place. Look at the pictures shown here to see the difference. Of course, once the freewheel or cassette is off the wheel there is no question as to which is which.
Shimano Tourney 7 speed Freewheel
https://www.ebay.com/itm/224922749090? Shimano Tourney 7 speed cassette
https://www.ebay.com/itm/385081675834
Why not simply exchange tires and tubes from one to the other? That's a lot easier. It seems like $45 just to switch a cassette is highway robbery. It takes less than 5 minutes and any bike shop will have the tools to do it. Maybe this bike shop is being mean because you bought the bike from Cosco rather than from them.
One more suggestion is to learn how to tell a quality bike from a mediocre bike so that you might be able to acquire a much better bike at similar cost in the future by looking for a higher quality used bike. You don't say how long your previous bike lasted before the repairs to it were so expensive that it made more sense to buy a new bike rather than fix up the old one. This is an entry level bike specifically made for Cosco by Pacific Cycle. It sells for $400 in the US. It comes in "one size fits all - medium" . Better bikes come in multiple frame sizes so you can get one that actually fits. Anyone who has owned and ridden a really good quality bike will tell you there is a world of difference between that and a throw away bike.