Let’s start with the shop. There should be no issue with going to a freehub over a freewheel. You’ll need a wheel with the freehub in it and a cassette. As long as it’s the same width as the original hub, it will just slide into place. If the mechanic or owner (or both) don’t understand that, it’s time to look for a new shop. And, although I’d rather support a shop, if they won’t do what you want, go buy one without their “permission”. It’s relatively easy to swap a wheel.
Now on to what you should be looking for. Your title is wrong. You don’t need a “better rim”, you need better spokes. Spokes do all the work in a wheel. Rims are just a convenient place to put the spokes and a place to mount the tires. If you can, have a wheel built (or build one yourself) with heavier duty spokes. DT Swiss Apline III are 2.3/1.8/2.0mm triple butted spokes. The heavier head resists fatigue better for us heavier riders. Quality Bicycle Products will build you a wheel with them. It’s not cheap but replacing wheels constantly isn’t cheap either.