What causes frames to break at the (rear) dropouts? The drive-side dropout and rear axle have broken twice. It's an old-style freewheel, not a freehub+cassette. (I weigh around 100kg, and ride a lot, and have been touring on hilly, gravel roads, with 15kg camping gear on the rack.)

The bike is an old (20-25 yo) hybrid Malvern Star (model "Elite"), steel frame, with 5 cogs on the back, and a freewheel. About 2-3 years ago, the drive side dropout broke, along with the rear axle (QR). I got new dropouts welded in, and the QR axle replaced with a solid bolt up (for $172 AUD).
They told me the axle "wouldn't beak". After a year or so, the rear axle broke again (which the LBS replaced). Then, about 6 months after that, the drive-side dropout broke again (EDIT near the chain stay) - not the weld, but the dropout itself, next to the weld.

I ride everywhere, and did several wilderness touring trips during that time. They were "on-road", but hilly, gravel roads (Bunyip State Park), and sometimes they're corrugated, sometimes water eroded, and ther were some tree roots on a rail-trail once, which I (mostly) manage to avoid. I wouldn't think they'd stress the bike that much, and wheel rims are perfectly OK - even though single-walled.

The LBS said it's because the freewheel stresses the axle, and when it breaks, the angle of the axle stresses the dropout, causing it to break in turn. They said it's the only cause of the break, and would not happen with a freehub and cassette. Researching online, I see the freewheel design does stress the axle. The guy now maintaining Sheldon's site agrees that that's how dropouts break; a couple of source only say it "can" break dropouts - but most don't mention an effect on dropouts at all.

Is the freewheel why my drive-side dropout keeps breaking?

Would a freehub + cassette really "solve" this problem, or would it keep happening? I want to go on longer tours, and don't want to get stranded!

Is there another solution?

Many thanks for reading all this! :-)

tyres: Schwalbe endurance, 26x1.50, inflated to 100psi (which they are rated to). Supposedly somewhat puncture resistant; but I got one on every tour.

dropouts: The replacements were forged dropouts (originals were pressed dropouts). It looks pretty strong to me, it's about 4mm where it broke, and about 7mm where the bolt goes.

hubs: after second broken axle, LBS noted slight pitting on the hub where the ball bearings run. Wheels are "Joytech", new about 5 years ago. They were the cheapest ones ($80 AUD, IIRC), single alloy rims. They look very well made (to me). The rear was a QR.
You already more or less answered your own question.

The reason is that in a freewheel hub the drive side bearing is close to the center of the axle. This gives the forces from your weight and pedaling much more leverage to bend the axle than on a Shimano-style freehub where the drive side bearing is located at the end of the axle. When the axle bends, it twists the dropout, which can also break.

Some other brands of freehubs solve the axle bending problem with a thick oversized axle. This could work with a freewheel hub too, but I am not aware of anyone who makes that kind of hub.