You are describing a child custody case. Whether it is a matter related to child support, conservatorship, possession, or visitation with your children a child custody matter is what you are generally referencing. This means that you will file a Suit Affecting the Parent Child Relationship and then proceed to serve your co-parent with notice of the lawsuit and then begin the case. It is possible for you to establish court orders related to your child even though you and your co-parent are not married.
For a Texas court to have jurisdiction over your divorce two things must be true. First, you must have been a resident of the State of Texas for at least the preceding six months prior to filing the divorce lawsuit. Second, you must have been a resident of Harris County (or whatever county you plan to file in) for at least the preceding 90 days. If both conditions have been met, then a Texas family court can hear your case. You can use utility bills to establish residency.
There are multiple ways for you to get a divorce in Texas. First, there is no rule that says you need to spend a lot of money to get a divorce. There is nothing in the Texas Family Code that states you need an attorney to file your case- although it helps (a lot). Depending upon the circumstances of your case it may be that your divorce could be wrapped up rather quickly, which usually means that you will spend less money in getting to that point. Finally, if you are on SNAP, have WIC or are on any other type of government assistance you may be able to apply for a waiver of your court costs associated with filing your case.
This is, unfortunately, a threat that some people make to maintain a marriage. Putting your child in between you and a divorce is unethical and harmful by your spouse, however. No, filing for divorce does not normally trigger a chain of events that sees parents not being able to spend time with your children. What she is describing is having your parental rights terminated. This takes a great deal of evidence to do and goes against the family laws of Texas as well as the inclination of most every family court judge in the state.
Not yet. This is a great idea and one you should follow through with once your divorce is over. The last thing you want to see happen is for you to pass away only to find that your ex-spouse is listed as the beneficiary on a life insurance policy and/or retirement plan. However, your temporary orders may bar you from changing or updating these items during a divorce. Set a reminder for yourself to do this as soon as the judge has signed off on your Final Decree of Divorce.