I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
What a judge is looking at in a custody determination is (a) how have circumstances changed since the court order was entered and (b) what is in the best interests of the children? You can report your ex to police if you know she's driving without putting your 5-year-old in a booster seat. You can ask the judge to give you permission to refuse to give the children to her if she arrives withOUT a booster seat in the car. That's something that would be worth the time, even if the judge didn't give you full custody, because it's for the child's safety. You're allowed to ask for multiple, alternate outcomes when you go to court.
If the children's clothing smells like cat pee, that's something that goes toward the mother's fitness to take care of the children. They should be taken care of, in clean clothes, not smelling of urine (whether human or animal). The judge could order her to take a parenting class and let the children stay with you until she produces evidence that she finished. You could also argue that cheating on her boyfriend by planning to marry another man goes negatively against her moral fitness to parent. Whether she's putting the children in actual danger depends largely on whether this man is ever going to be released from prison - if he's being paroled and she's planning to move in with him, that would be a stronger argument against changing custody than if he's serving 10 back-to-back life sentences. Also, check to see if your original court order has a mortality clause that prevents her from having unrelated overnight guests while the children are with you. (You can also ask that the judge add one.)
You can ask for full custody, and it's possible that you'd be able to get it. But because the judge has discretion to enter other modifications to the court order for your children's health and safety, it likely would not be a waste of time to go back to court, even if the mother gets to keep some joint custody or visitation.
It's important that you are 100% satisfied with my courtesy and professionalism. Thank you.