How to eliminate outdoor rats?

We've been having rats in our back yard for 3yrs now and it's costing a tremendous amount of money to repair the damage they've done and to kill them off. My neighbor has fruit trees, so there is nothing we can do to prevent the food source as he won't cut them down. His newest one, planted right under 4yrs ago in his backyard (which is our problem tree) is planted only 4feet away from our fence. The rats eat in his yard and take shelter in ours. We can't eliminate their shelters as they've used our hot tub (3 motors have been replaced already due to chewing wires), our BBQ pit (has been replaced twice, but begging husband not to replace it again as we just noticed yesterday this new one has gone to sh$t as well) and our shed since we need it to house our lawn tools. The hot tub & BBQ pit is in our screen patio so of course constant replacing of the screen is needed...as you can see I'm just FED up! My daughter can't go in the backyard anymore (scared of her touching something contaminated) and since I'm deathly afraid of rats I can't go in the backyard anymore without my husband being there...and since he works away 2wks out the mouth, I'm screwed! We've purchased every type of trap there was. The glue traps weren't strong enough and the wood/spring traps failed on a few rats that my husband had to shoot with a pellet gun to kill them as they couldn't get out the patio with a trap around their neck to escape. We now have the T-Rex traps and although the pellet gun has stayed in the closet now...it seems as though the rats are to smart for these traps! We've only killed a hand full, but there is always poop around the trap as they just walk by it. BTW, peanut butter is our main bait used. There has been this stray cat hanging around (huge, bad a$$ cat) since my dogs have passed away and I've been feeding it to keep it coming back for more but of course it can't get into my patio or in my shed. I was told to NOT repel the rats from my shed or patio as they will find their way into my home...which I just can NOT allow. What can I do to completely repel them from my yard. I am assuming the rats are crawling up my 6' wooden fence to gain access to my yard as I don't think they can go under it or between the boards (boards are pretty swollen tight). Is there anything that I can spray on my fence to prevent them from even entering my yard once? Obviously a "little spray bottle" of something won't be enough! It needs to be a massive amount of liquid to cover the entire fence and possibly penetrate the wood.