In Caroline's response I understood that neither women or men could remarry after a divorce, because you can only be married in church and the church doesn't recognize divorce.

That is exactly what I did mean. I have not found any references, in Austen or in history of her time which suggests that a divorcee of either sex could marry again. I'll admit that I have not gone looking, either, but it's based on my knowledge of the C of E which still doesn't like to marry divorcees, though it will, at the priest's discretion. Before about 1960, They never married divorcees- the parties concerned had to have a civil wedding or none at all, or be married in a different religion entirely. Mrs Rushworth has to remain alone (except for Mrs Norris, of course) for the rest of her days.

As to why anyone bothered getting a divorce, I'm not sure about that either. I assume it's as you say, Barb- to release themselves from the financial obligations to the spouse. And since women almost never got a divorce grated in their favour, it allowed the man to walk away, and the woman was left pretty destitute.

This sounds like something that Lawrence Stone would write about........