Is Nick (if he managed to get his license back) able to represent Kayla in a civil suit against Aaron if Aaron has a restraining order against him?
There are two types of conflict of interest, waivable and non-waivable, and two categories of status, potential and actual. There's clearly a potential conflict of interest here. A waivable conflict of interest allows the attorney to advise the client of it and continue the representation at the client's will. Nonwaivable conflicts can't be waived even knowingly.
(To pick an example from criminal law, you can represent two criminal defendants in a case and while this is often considered a precarious situation, it can be done ethically, as an example, if both defendants are on the same page factually, e.g. neither of them did it and some third party did, like in My Cousin Vinny. However, if the situation changes such that they're now both accusing each other of having done it, this instantly changes into a nonwaivable conflict and the attorney must withdraw and both defendants must seek new counsel.)
I don't know what this would be. Generally, testifying or other behavior in court is privileged against such orders, otherwise you couldn't testify at all in your own defense, and on top of that, you could just get a series of restraining orders against opposing counsel to deprive your opponent of a lawyer.
Obviously, what Nick would be doing, that is, exploiting his wife to use her as a proxy in litigation, is profoundly unprofessional and unethical, but you'd have to prove that to disqualify him (unless the judge just outright refused to allow it).