Trying to wire my inverter output into my RV panel
No.  You can't wigger-jigger it like that.  I've been saying this a lot today, but if one thing is broken and wrong, it's best to fix that first - the other problem may take care of itself if you do.  

You need a proper interlock so that it is physically impossible for any of the prongs on any plugs to get "lit up".  

If your breaker panel lends itself to interlocks

You're on the right track with breakers where only one is on at once, but you must have physical interlock to make "both on at once" impossible. 

Some models of breaker panel have very simple, inexpensive options for interlocks.  Such as Square D "QO" and Siemens/Murray.  (Keep in mind you must not mix-and-match breakers and panels; use only breakers listed or classified for that panel). 

If this is not feasible, there's another way. 

Use a plug/socket as an "interlock"

Presumably your RV has either an inlet, or a short cord-and-plug, which you plug your extension cord into in order to reach shore power.  

OK, so you build a virtual "extension cord" from your inverter to that inlet/plug.  On shore power, you plug the RV into shore power.  On generator, you plug the RV into the inverter instead.  That's pretty simple, isn't it?

The trick is, you build this "extension cord" right into the RV, using in-wall wiring methods.  One end is a plug-and-cord going into the inverter, obviously.  The other end depends. 


If the RV has an inlet, then you have a cord-and-socket which is just long enough to plug into the inlet (and too short to worry about it dragging on the ground).  
If the RV has a short cord, then you have an outlet within reach of it.  


Either one simply goes straight to the inverter.  

Now the procedure is simple: whenever you unhook from shore power, you connect that cord so you are looping over to the inverter. 

Use 240V, 4-wire connections

I hear you saying you're using a 3-prong connector with a ground. That doesn't make any sense unless the RV is very small and uses a TT30 connector.  I expect your RV is 120/240V split, and needs 2 hots, a neutral, and a ground.  I suspect you have inadvertently connected neutral or ground to a hot wire, and that's why it is lit up.