When the accused leaves a false impression during his DIRECT examination as to his prior arrest/convictions/"trouble" with the police, he has opened the door to an inquiry by the State as to the validity of his testimony. Prescott v. State, 744 S.W.2d 128, 131 (Tex. Crim. App.--1988).

What if I get him to do it during CROSS-examination?

Example: Defendant is on trial for DWI and has a prior conviction for DWI. I ask him during my cross-examination, "Do you have a problem with alcohol? Are you a safe driver? Do you allow alcohol to affect your judgment to the point that you allow yourself to be a danger behind the wheel?"

Assuming he answers "No" to these questions, I would argue that the prior conviction is admissible because he's left a false impression with the jury (he's NOT safe, he DOES have a problem with alcohol, here's the prior conviction that proves it, etc.).

All the case law I've come across deals with the defendant opening the door on his priors during direct, not during cross.

I'd appreciate yall's thoughts!

I think that would be tough. See Shipman v. State, 604 S.W.2d 182, 183 (Tex. Crim. App. [Panel Op.] 1980):
"Whether appellant had been intoxicated two years previous to the offense in question is a matter which is not legally relevant to the offense for which he was being tried; the State would not have been permitted to introduce such evidence as part of its case tending to establish appellant's guilt of the charged offense. It was therefore error to permit the State to contradict appellant's answer on this collateral matter by showing he had previously been convicted of driving a motor vehicle on a public highway while intoxicated."

You can't open your own door. So asking him questions intended to have him open the door to impeachment material is not going to work.