If I leave the state with my kids for a couple of weeks to give my husband space, can he use this against me?

You're fine as long as it is temporary and not a permanent relocation. You should let him know where you are going with the kids, that it is just for a few weeks and your telephone number, otherwise he might file a motion with the court claiming that you have taken off permanently with the kids. This response is intended to provide general information only and is not a substitute for speaking to an attorney. This response does not create an attorney client relationship between the Anita Webster, Esq. or Webster & Associates and the readers.

I think you just need to explain to the court if the issue comes up. You have a plausible story and you do not intend to leave permanently.

Technically, until the parties truly "separate" (which involves not only physical separation to live in separate residences but also with the intent of either party to separate/not resume the marriage which sounds like the latter might not be technically present even for you), then the courts don't tend to get involved in such private matters. But incident to separation, yes drastic moves or even temporary departures like that can certainly come into play/be argued by the other side though, without any agreement or court order in place you would not really be violating anything either. You should consult with an attorney as there may be another way to "get his attention"

What do you care if he claimed you abandoned him. That itself has no effect on property distribution in your divorce and only adversely may affect you if you try to stay in Texas with the kids, leaving the impression that you are running away with the kids.