There are a couple of ways it can be done. A simple statement, notarized (you each keep an original) is easiest, but she can claim you didn't make the payments after you signed. Setting up a joint bank account that is titled "child support" where you make the deposits and she can withdraw can work, and show proof of exactly what you deposited. The best way is to have a child support order, so the state keeps the records and no one challenges them.
If you marry woman 1, then marry woman 2, then you are guilty of bigamy (it doesn't matter what name you use). When the marriage to woman 1 ends, the marriage to woman 2 immediately becomes a valid marriage. (it is void until then). If you want to be sure, either remarry or file the certificate the previous answer suggested.
You should be able to modify the Order to have him pay support. The adult children are out of the equation, and don't effect the support. Contact a good family law attorney in your area to explore your options.
Technically, since Texas is a community property state, 1/2 of your refund is his and therefore subject to seizure. Practically, if he is not on the return, they will probably not garnish it as they track things through his social security number. If they do garnish your return, you have some defenses and should contact a good family law attorney in your area to help.
A child can legally decide where she/he wants to live at age 18 (when no longer a child). At age 12, if someone requests it, the Judge has to interview her, but the Judge will decide custody issues based on what the judge thinks is best for the child. Most judges give a lot of weight to what a 16 year old wants, but they don't have to do it. For custody to change, a modification must be filed and granted by a judge. If you think your mother will fight the change, then I would not suggest...
Abandonment is leaving your child somewhere with no intent to return. One day is usually not enough. Has there been other CPS cases? Get a good family law attorney. CPS is not your friend.
Good luck to you.