I am also a big encourager of telling children the truth, because if you do not, they will blame themselves and come up with MUCH worse. However, since she is only 3yo, you would need to tell her in an age-appropriate way. Remember, she does not have all the tools to cope and understand that you do!
So in my humble opinion, if she specifically asks (like "Where is Daddy? Why doesn't he live here anymore?") I would reply something like "Well sweetie, your daddy is at his apartment right now because I believe mommies and daddies should only love each other, and I think Daddy may disagree. So right now, I miss him and I'm waiting for him. Do you miss him too? Want to wait for him together?" This teaches her what YOU believe is right and wrong without necessarily speaking for your H; it tells her how you feel and what you're doing, and then gives her a chance to say what SHE feels and what SHE wants to do.
I get it--she's only three--but this gives her a place where she is safe to express her fears and feelings, and that's pretty healthy, even at three. And just to be clear, this is my own personal opinion and may not necessarily be anyone else's! LOL