mother of two boys here in Texas. Father lives in California and wants joint custody. Can he file in Texas? What are his chances of succeeding?

If there has never been an order in place regarding your children then it sounds like TX would be considered the home state of the children and all litigation regarding custody and visitation and access should be tried in TX.  However, if there is already an order in place from another state, then that state would have to relinquish jurisdiction in order for TX to exercise jurisdiction.  In terms of your question regarding joint custody, I think you need to understand the terminology used by the Courts in Texas.  We do not give a parent "custody."  Texas will appoint parents, or in some cases, non-parents as conservators of the children.  The most common type of conservatorship ordered is called joint managing conservatorship.  However, this label can mean many different things.  If the parties live close together it CAN mean that you are both equals in terms of decision making and time with the kids.  But most of the time one joint managing conservator still has the majority of possession time with kids and the other parent visits with parent via a standard possession order schedule.  I say all this just to let you know that even if your children's father is awarded joint conservatorship that doesn't necessarily mean that he would not have to pay child support.