You're in a financially lopsided marriage. The numbers in these cases can be quite shocking. You need a lawyer. She's actually low-balled alimony. If you can make her $1000/mo request stick while lowering CS to guidelines, you'll have done well. Make sure there's an end date set for your alimony payments and try to get it designated non-modifiable.
Having half your paycheck siphoned off does create a hardship for you. From her perspective losing all *her* "income" creates an even greater hardship for her and *her* children.
I was in a similar situation as you and, you know, in a messed up marriage, I felt I had lost control of almost all my paycheck. I tried to tell myself to be delighted that divorce restored my control over fully half of it and after a few short years, most of it. That didn't really take the bitterness out of it though.