Wow, no pets? You're going to have a difficult time finding a park in Yuma that doesn't allow pets. But, there are a lot, and I mean a LOT, of RV parks in Yuma, so you may get lucky.
The reason for allowing pets is many RV owners have pets.
As for aircraft noise, you realize the Marines have a base there and they fly very noisy jets?
As for trains, the first "transcendental railroad" went right thru town and the trains still use those tracks.
Your best bet might be to the south of Yuma at one of the older parks since they are further from the airport (Marine base) and the railroad. I can't offer any names since I just don't remember them. The parks out in east of town, called Foothills, are closer to both the airport and the railroad tracks, although the tracks at this point are north about 1/4 of a mile or more.
Holiday Rambler Navigator DP, Hummer, and Honda VT1100C Shadow