The only thing preventing you from teaching as a PADI instructor in an SSI shop is the shop owner. He or she may or may not want to have both agencies being taught there, and he or she may or may not choose to hire you at all. You should first find out about the chances of employment, and then ask the person (hopefully) hiring you what your best choice would be. You may have to get certified by SSI to work there.
If you are not going to get hired in any event (it may surprise you how likely that might be), as a PADI pro you can work independently. For a new instructor, that might be very difficult. It depends very much on where you live. I live in Colorado for most of the year, and if I had to make it as an independent OW instructor here, I would quit. The local infrastructure is not set up for it. In contrast, I live in Florida for a few months each year, and I could do pretty well as an independent instructor there. I wouldn't need a big equipment inventory because local shops want me to use them, and they will rent all the gear to my students and give them tank fills at a good discount. (Local Colorado shops will not rent gear or fill tanks for someone else's students.) Dive boats want me to use them, so they will give my students discounts on rides and let me go for free. (In Colorado, for half the year there is little to no local diving, so I can't complete their certifications at all.) I make it as an independent in Colorado only because I specialize in technical diving. I have almost no competition, my students have their own gear, and local shops will work with me because they don't offer tech, so I am not competing with them.