I wouldn't want to weld the stabilizer to the frame. These are replaced from time to time, and welding one in place would make that much more difficult.
Much easier would be to just move it over a tad. The outer mounting point will be easy to move - all you need to do is drill new holes and carry one. The inner mounting hole might be a little more difficult depending on which type of stabilizer you have and how wide the frame is that it mounts to. On my stabilizers there are two holes at the inner end - one on each corner. If I needed the whole unit could be moved a little and the other hole used.
Another option for the inner mounting bolt is to have the welder add a tab on the end of the jack so you can move it over a little so new mounting holes can be drilled.
If you weld the stabilizer, you'll have to deal with the belly pan somehow.
Welding to the frame can be done, but like in any vehicle the electronics need to be protected by disconnecting the battery. I'd also pull the main power feed to the
12v panel and pulling the shore power cord as well.