Unless she's blind, or just an idiot in general, she'll see right through that. I do not think it will do you a bit of good and if I were the unfortunate recipient of that letter of lies, it would make me hate you even more.
I've read some of your posts. I'm sorry you're going through such a rough time. What kind of proposal were you presented with? You don't absolutely have to agree to any proposal. The only thing that is absolute is a court order. You will be required to pay a certain percentage of your income for child support. It doesn't matter what you're "willing" to pay, it'll be what the judge orders you to pay and the judge goes by basic state guidelines.
As far as the insurance goes, if your daughter's mother has low income insurance for her through the state, you will be ordered to place her on your insurance if insurance is available to you through your job. That way the state will not have to provide services to your child that you should be providing as her parent.
Good luck.
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~ Any man can be a father, but it takes someone special to be a dad. ~