@Eric_Phillips I am not quite sure what you mean by a wood and a vinyl post in the same concrete. Two holes, one blob of concrete, or one hole with two posts in it. Or something else? Do you have a photo?
I've been pulling out and replacing old posts in the old concrete for a while now in an ongoing roadside project. I don't know how universal my method is, but FWIW here is what I have been doing.
Tip #1 age the new posts until they are really dry. (Preshrunk)
One method I use is close to
@not2old's. I use big drills to chew up the wood and long pry bars to break it into pieces and use a shop vac to get the crud out of the hole. I try to line the drill holes up to split the post into halves or quarters (ish). Then drive a new pressure treated post down the old opening.
Method #2: when the post is either in good shape or really bad shape 12" or more down, I add water and drive a new post down on top of the old post, which gets pushed out the bottom.
I back fill any gaps with mortar and then caulk to keep water out, as I think, like
@EddieWalker, that ground rot is accelerated by standing water at the post.
If you don't have access to a post driver, I get the old wood post out, and pour concrete supporting a metal wood post base, or a metal post, encased in wood for looks.
All the best,
Peter