You are shooting yourself in the foot - never offer pay her more than you have to. You said you decided to pay her halfway between your offer and what she is demanding. What you have effectively done is increase your offer. You are demonstrating that you can pay this amount and setting the status quo, so now you will have to negotiate above that. Your goal is to pay her as little as possible, and demonstrate a status quo that she can make ends meet on that amount.
First, dont take any action like this without clearing it with your lawyer. Stop the payment now. If she freaks out, blame your lawyer.
Second, I would highly advise you to pay child support now, but fight tooth and nail against paying alimony. If you fight for yourself, and have a good attorney who will fight for you, there is a very good chance you could get out of alimony so long as you dont make mistakes like voluntarily agreeing to pay her too much money.
