We don't know much about Anne, but what we do know suggests that they didn't much like each other. Their daughter was born only a few months after their wedding; it's pretty clear that this was a forced marriage. Shakespeare published a book of sonnets, many of them about love, and none of them about her.
We know a fair bit about Shakespeare's life in London, and pretty much nothing about his life at home. The whole "second best bed" thing is weird (as much as historians try to put a positive spin on it).
None of this directly influences my work as an actor and director. The plays are the text, as it comes to me, and I practically never look at the author himself to find the connections between that text and the audience I'm performing for.
Still... I suppose I always have that in the back of my mind, somewhere. Thinking about the author a little differently (even if only as a hypothetical) surely influences me. If nothing else, Shakespeare's relationships with women are, uh, fraught. Sometimes he seems really cynical and misogynist. Sometimes, he's writing great female characters and giving them real agency.
As I said, it's up to me to see the words and figure out what effect they'll have in performance. But it will probably end up influencing my options nonetheless.