It's complicated, but any DNA test you get on ancestry or like service is not going to be definitive. If you are mostly English with a spattering of other nationalities (like me British 75%, Ashkenazi 17%, Italian 5%, German and Norwegian >2%) and she is cheating with a guy that fits your profile. Plus if your kids are girls, the test results will be all over the place, since half their mothers DNA is lost. If you have boys, then you can DEFINITELY determine who your sons are since boys ALWAYS inherent ALL the "Y" chromosome DNA from you. Girls will be all over the place unless you pay for an expensive DNA analysis.
If you think your wife is cheating on you, there is a very good chance that she is. Trust your gut and like
@AJ84 said just hire a PI.... Not that it matters, my ex was the ***** of Babylon when I was in Afghanistan, none of that mattered in divorce court. We've been divorced for 10 years now and I'm still paying for her BS mental heath treatments.... She'll just go to court and cry that she is sick and needs 'help', and the judge will make you help her.