Okay, it sounds like there are two problems, one being the 110VAC for the TV and another for 12VDC for the lights. That leaves me to recommend working one issue at a time to avoid lots of confusion!
On the breaker that pops up, that isjust a much smaller version of the breakers with hanldes we find in other spots and there are two reasons they will not stay pushed in.
One is that it is worn out but the other is becasue there is a drain or fault of some sort which makes it pop!
But on the good side, we do get good schematics for botht eh 12 voltand 110 AC on your RV, so how are you set for working on things?
Have a meter and know what to do with it or no experience?
We can send you to the info needed on where to find the drawings if that is something you feel ok with-- or we can do the looking and let you do the work!!!
Got a choice of which you want to work on first?
Looking at tyour pictures and this drawing:
https://www.winnebago.com/Files/File...999/129781.pdf
It looks like you have a 30amp RV, correct? But then we may need to sort if it is US or Canada version???