Without a court order, you are obligated to pay nothing, including child support. What you've already paid will NOT count toward any support that ir ordered, it's considered a gift.
Is your name on the mortgage to the house? And I'm confused by your use of the term **equity line** Is this an open line of credit collateralized by the house?
Have you checked to see what you should be paying in child support by looking at the state statutes?
Essentially, you're at ground zero. Your agreement does constitute a separation agreement, now you need to memorialize it in a divorce decree. If you don't want to pay on the equity line, that's something that will need to make it into the court order.
You can simply stop paying on the equity line with little or no penalty, I would think. Continue paying the agreed upon amount for child support but make sure it meets state guidelines.