You need to formalize this as soon as possible. "Understandings" lead to misunderstandings.
Hire an attorney, if you can afford one. If you can't afford one, see if Legal Aid can help you find one. If not, then you need to plow ahead and file a Suit Affecting the Parent Child Relationship (SAPCR). The county law library has the form you'd need to file the suit.
Where it gets messy is in the order that the court signs. You need for that order to be exactly right in terms of giving effect to what the parties want to do. This is why folks suggest you hire an attorney. 15%-20% of my practice involves cases where the parties did everything on their own, saved on legal fees, and now they are back in court, spending twice as much to fix things.
In answer to the child support question, prospectively waiving child support forever is hard to do in many courts. No one knows what the future brings and what the children's needs are going to be. Most of the courts I practicein would not sign such an order. Some would let it slip in, but counting on an inattentive judge is not a smart strategy.
Child support is ordered based on the relative resources of the parties and the needs of the children. If two people are splitting possession 50:50 and they each make about the same income, it doesn't make sense for one to pay support to the other, except to defray health insurance premiums, etc. But facts that deviate from that perfect balance will lead to different results.
Hire an attorney today if you can.
Formalize all things through the court process with using attorneys NOW. I read countless accounts of situations that start out amicable with the baby under a year or 18 months. Then, things tend to sour after on or the other spouse meets someone new and gets remarried.
Do this right now, the first time, and get a joint custody arrangement in place through the court order process.
Good luck to you.
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