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This sounds like Shazam!
only there was no woman and I don’t remember a dog. It aired in tandem with The Secrets of Isis, which definitely did star a woman, so maybe you got them mixed up in your head.
Sorry, I remember it is animated.
If a chicken crosses the road and nobody else is around to see it, does the road move beneath the chicken instead?
I doubt this is it, as you'd probably remember if it was a Scooby Doo show, but in the 80's we had "The 13 Ghosts of Scooby Doo." The only characters from the original series that were in this one were a man (Shaggy), a woman (Daphne), and a dog (Scooby), and they had an RV (The Mystery Machine). The show also had Scrappy and an all-new character called Flim-Flam, which you don't mention in your recollection.
However, just in case, here's the Wikipedia article on it:
http://en.wikipedia.org/wiki/The_13_Ghosts_of_Scooby-Doo
There's also Goldie Gold and Action Jack, with her dog, Nugget. They don't have just an RV, though. Her money gets them all sorts of interesting vehicles.
https://www.youtube.com/watch?v=of77cC6g94E
Yes, it was Goldie Gold and Action Jack. Thanks.
If a chicken crosses the road and nobody else is around to see it, does the road move beneath the chicken instead?
A series, most likely from the 80s. One man, one woman and a dog, maybe a retriever. Uses an RV. Fight bad guys. That is all I can remember, I'm in kindergarten at that time.