Your facts are very confusing and you will need to consult with an attorney to sort this out. If there was a child support order in California, then California has continuing jurisdiction over your child. If you are sole managing conservator of your daughter, when did the Court grant you this sole managing conservatorship? When you say you were served with child support, were you served with a motion for enforcement of child support? Where there temporary orders set on your divorce case that originally gave your husband custody of your daughter and ordered you to pay child support? You need to seek the advice of counsel licensed in California if this is where your current child support case is. That state has jurisdiction over the divorce, custody and child support matters.
The information provided is not advice but a legal perspective and you should schedule a consultation with the lawyer of your choice.
If your divorce is pending in CA, you need to talk to a CA lawyer about this. It sounds like dad is trying to pressure you with the child support obligation. It also sounds like you do not have an attorney in CA. You need to find an attorney to represent you in CA and get your divorce completed. The child support issue can be worked out in the divorce.
I recommend that you consult with an attorney regarding this matter.