I had that happen. Only thing is when you are in a big coach driving you think it's something to do with the handling of the MH or just the wind.
Mine turned out to be and IMHO in a lost of cases it was the tow bar. Brand New Blue Ox. The arms were not locking in place properly. When I took it in they would check the bar and swear there was nothing wrong. Foght it for hundreds of miles.
Long story short I 'finally' found a competent dealership in MO that 'after saying I was simply just going to buy another new one for my safety' really took a good long hard look at it. We opened up the area for the lcck and could see it was not engaging properly so when you took off after checking it it would slip. Hence forth the swaying of the toad. Even thought it was engaged during routine check of hooking up.
Blue Ox still said I was crazy and wrong but when thy found out I was serious enough to buy a second one they did tell the dealership to give it to me for free.
Pulled out with the new tow bar and the coach tracked straight as an arrow. Yup I was right that it was a bad tow bar!:C