I asked my UKC husband about your situation and hopefully I'm relaying this correctly. (He's Scottish so depending on where your partner lives, YMMV.)
In short, no, not like in the US. If you go to court, the court can request records. But you as a private citizen will not have much recourse to a criminal records check without the court being involved. Unless you can find something on Google, you'll have to rely on the judge or possibly a lawyer.
That being said, I just poked around Google for a few minutes and found websites that offer background checks. However, they don't seem to include criminal history, which I think is what you are looking for.
Best of luck to your partner. It sounds like a terrible situation and I hope she and her kids are safe and healthy.