Warren,
I haven't done as much welding as a lot of guys here, but I did weld on nuclear submarines for a little while and also did a fair amount of maintenance welding years ago. I have gas, MIG, TIG and stick welders and a plasma cutter for my own projects and wouldn't hesitate to make the repair you describe.
The prep work here is as important as the actual welding, IMO. What I would do is "V" the two pieces to give about a 45° angle, all the way to the bottom, then grind the ceramic coating off for about 1/4" back from every place you'll be welding. I'd put the wide part of the "V" facing down so it doesn't show. Take just a LITTLE weight off the back of the pipe by placing some kind of support under it. Bolt the broken end of the bracket into the rubber frame mount, then align it with the end still on the pipe and clamp everything in place with a couple of C clamps and a piece of 1/4" or so thick scrap steel. If both pieces don't line up perfectly, see below. DON'T use the C clamps and scrap steel to pull the pieces into alignment! Now remove the pipe and take it to your friend at the welding shop and he can take it from there. Just be sure he clamps the ground on the bracket and insulates the pipe from the welding bench.
The rubber cushions on my first set of rubber sidepipe mounts cracked the first season I had the car. When I replaced the mounts, I found that the holes in the brackets and the frame were about half a hole off, which placed a lot of strain on the rubber cushions. I "ovaled" the holes in the brackets so they would bolt up without any misalignment and these ones have lasted almost 4 years.
I think there's an article on SCOF or CC regarding reinforcing the sidepipe brackets but I'm not convinced that's necessary. If you think that's what you want to do, however, now would be the time to do it.
There are a lot of ways to get the skin off the cat. The above is just my opinion but that's the way I'd do it. Since you asked...
Good luck,
Lowell