nope, you don't need to tell her what you want, remember her feelings are all over the place, she is the one that wanted to separate from you, she wanted you to move out, etc.
Telling her you want the marriage to work may go against her current feelings which are still too new & fresh. Remember she wanted to separate and you are telling her you want the marriage to work, two different things, remember the stance about agreeing with her.
You don't have to tell her anything, definitely not that you want the marriage to work out.
Yes I totally agree about ending a conversation with your spouse when they start getting nasty, pretty much like "I'm not going to reward your behavior with my attention, I have no problem talking to you when you are calm and more mature"
