Also, if Anakin had confessed to his relationship with Padme--and that he was the father of her unborn children--he would have been exiled from the Order. He would have had to face a choice: either lose his position or lose his wife.
I very much doubt that they would have exiled Anakin just like that. Considering his Chosen One status, I think it's more likely that they wouldn't want to piss him off and would sit on the issue for a while, at least until Sidious was found and stopped.
"There is something going on in time and space, and beyond time and space, which, whether we like it or not, spells duty." -Winston Churchill
"For of all sad words of tongue or pen, The saddest are these: 'It might have been!'" -John Whittier
"Apathy is death." -Kreia