Joint custody is just a term in the State of Texas. It does not mean that you are even having 50% possession of the children.
Many times the parties agree to joint custody but then one parent receives all the rights and duties of a "sole managing conservator".
So don't rely on the term "joint custody" to protect your rights as a parent.
You need to look at the rights and duties and the amount of time that you spend with your children.
Generally, in the State of Texas, the non-custodial parent (aka non-primary parent) can elect an expanded standard possession order so that the parent has possession of the children 48% of the time. But that does not mean that you won't pay child support.
But don't sign up for an expanded possession order unless you can truly do it. Otherwise, you forfeit your visits with the kids if you don't pick them up when ordered to do so.
Talk to an experienced family law attorney in your county about your options.