I have a GFCI outlet that is wired to another non GfCI outlet. So when either has a problem, they will trip off. My question. Can I reverse these outlets? Let's say the GFCI outlet is on my left and the non-GFCI outlet is on my right, can I switch them and put the non-GFCI outlet on my left and the GFCI outlet on my right?
The physical location of the two devices does not matter, it's just how the GFCI is wired. If you wire a GFCI one way, it'll protect every receptacle after it - if you wire it another, it'll only protect itself. If you simply want the GFCI to only protect itself, then just switch the wiring and leave it where it's at. However, if you'd like it to be in that new location and still only protect itself, then you can switch them and just wire it correctly.
However, there could be a reason behind why the plain receptacle downstream is protected. If it's in a location that, by code, should be protected; then it should be protected. If you don't like them both flipping at the same time however, then you could flip the wiring as shown in the above image and get a second GFCI receptacle and wire it in where the plain receptacle is now.
Again though, like the comments mentioned, if it's supposed to be GFCI protected and you're constantly having them flip.. I'd recommend putting in a second GFCI.
The problem is the physical constraints of wiring. Wiring is not a loop (in the US). GFCI's are not magic. In this circuit, the outlets are "daisy chained" - power comes from the service panel (breaker box) to one outlet, then to the next, then to the next. There's an "upstream" (toward the service panel) and a downstream. A GFCI outlet can only protect other outlets which are downstream from it.
Suppose the chain has outlets A B C D, all in the kitchen. Outlet A would be the GFCI, protecting outlets B C and D. Suppose you swap outlet A with outlet C. Now, A and B are not protected by GFCI, outlet C is the GFCI and it protects outlet D. For A and B to be unprotected is illegal under Code and dangerous.
Another option is to replace the circuit breaker feeding this string of outlets with a GFCI circuit breaker. Now it doesn't matter what the outlets are. You are free to use any type of outlet you prefer. Installing a GFCI breaker will require working inside your service panel, which may have always-on 240VAC.