Hopefully Venditti will get to explain all of it on a JSA run.
spoilers:end of spoilers
Maybe Carter and Shayera decided to go underground for some time, so they would not mess with their other lives? They can even launch a book "The Secrets Adventures of Hawkman and Hawkwoman.
About the Hawkwoman portrayal, I believe it was a combination of lack of pages and having to resolve the plot of Carter fearing death.