******EDITED********
Several people are under the mistaken idea that Texas State law doesn't allow for overnight visitation for children under the age of 3. That is NOT the law. The law gives that discretion to the judge on the case. Overnight visitation usually IS granted unless there is a reason the judge finds strong enough to not allow it.
****************************************************
First, I can't believe how many women still believe children are theirs and fathers somehow don't count. That simply floors me. I am finding most of the responses saying child support... yes, YES YES.. go get it that's yours! But then saying don't allow him to have the kids... amazing. Children's well being depends on both financial needs AND emotional needs being met. And that means a good, positive relationship with BOTH parents.
What is in your divorce decree? THAT determines what happens. Standard papers usually involve child support which is figured at a percentage of HIS income NOT "HOUSEHOLD". The new wife's income is NOT figured in AND she can file an injured spouse form on their income taxes which will allow them to keep half of their income tax should that ever be garnished. Yes, he should be paying child support for his children. Though in one breath you state that's not what your after and in the next breath you go on about the things he's buying. Making you sound a tad jealous. Which by the way, puts you in the same category as your trying to make his new girlfriend.
Second, both father's and children benefit from visitation. At 2.5 it will be harder than the 8 month old but they do adjust. It will be tough at first but they'll get into the mode pretty quickly and will have an easier time of it than if they were older. My husband's children have been doing this since they were 2 and 5 months old... very similar to your situation. They are fine and nearly grown now. It didn't hurt them at all. In fact, it was great for them to have a relationship with BOTH parents.
Visitation cannot be denied whether he's paying child support or not. Speaking badly of the other parent to or in front of the children is also not accepted in the state of Texas and children can and have been removed from the offending parent so be careful of that.
Just as there are rules to a marriage and making it work there are rules to making a divorce work as well. Don't become a bitter, controlling, use the kids kind of ex wife. Be respectable. understand that children are BOTH yours and your ex husbands. They are not just YOURS.
You don't say how long you were married, how long you've been divorced etc. Be the bigger person, understand a, she's young and going to be insecure. That's also normal in the early stages of second marriages. It will ease up as they solidify their marriage more. This is a growing period for all of you. You all have to learn a new way of doing things.
If you're concerned about not knowing the woman, pick up the phone and schedule a meeting with all of you. That way you can get to know one another. Make it in a non public, yet neutral place. Work out agreements on how the children are handled. Welcome her into his life and your children's life and show her there is no reason for her to feel insecure. That you don't want him back and you're happy for them. Being young doesn't mean incapable. I was 23 the first time I was a step mom and I was a good step mom. So much so that the ex wife didn't want to let him see his child after we split up. I had to convince her it was still what was best for their child.
I'm both a step mom and a biological mom. We have also had custody of my step children for 3 years. I've seen this from every angle. The children see their mother for regular visitation (whether they want to go or not) even though she has never paid a dime of child support. Funny thing is, she damn sure thought my husband should pay child support when she had custody. But now she doesn't think she should have to.
Encourage a good relationship between the children and their father. ALL studies show that is a very important relationship for kids. On top of that, encourage a good relationship with them and their step mom. Eventually, they will have a step dad and you would want the same for him.