Is the vise you are repairing the one sold by HF for about $70? A friend gave me one that looks like yours. It came from HF. It was broken in exactly the same place.
I'm not a formally trained welder, but I did stay once at the Holliday Inn express once. That's suppose to make you smarter, but I don't think it helped me.
That said, I took the broken vice apart, used wire brush on grinder and cleaned the broken parts. Put vice back together so the pieces fit perfectly. Then I spot welded it with a 6011 3/32 rod and 90 amps to burn it in. Took it apart and made about 4 passes. The round metal shaft looked like it was pressed in the jaws, not welded. So I used a little more heat to burn it in. Seems to be holding. Only cost me a few rods. I'm sure someone will give me a toung lashing for using a 6011 rod and not doing it the right way, but it worked. Vise was going to the recycler before I welded it. The guy didn't want his vice back, so I have an extra one.
Don't you find it odd that 2 vises broke in exactly the same place?
I'll post back when my weld breaks.