"After the colonies gained independence, states joining the union liberalized their divorce laws, as did the associated territories, with many permitting local courts to grant divorce. A few retained authority to grant divorce at the state level. In Virginia, for example, petitioners had to apply to the Virginia General Assembly for a divorce, and during the first thirty years of statehood, no female petitioner was granted a divorce.[1]"
So it really looks like Virginia was the exception and not the rule. It wasn't illegal at all and there was a legal framework for how it worked which, again, suggests that the initial claim that it was illegal was incorrect
https://en.m.wikipedia.org/wiki/Divorce_in_the_United_States