How can you find out what? Why she's texting him? If he has something improper going on with her? Ask him. "Why is she texting you after hours?" It's a simple enough question, and if he's not doing anything wrong, he shouldn't mind you asking it. Sure, his business is his business, but the texting is happening after hours during your family time, so you have a right to ask.
But before you ask him, I wouldn't necessarily assume the worst, unless of course he has given you reason in the past to do so. You say this woman is a "known swinger" -- known how? To whom? Did she tell you this herself? Or is this just a rumor that's been bouncing around disguised as the truth? If it's true, could you please get her phone number for me? Kidding.
You also say they work closely together. Is his the kind of job that would necessitate after-hours communication? If not, if he's a landscaper or the fry cook at Jack In The Box, then yes, you might need to worry.
Really, though, all this is moot. Just ask him. How do you do so without being accusatory? Don't accuse him of anything.
Just ask him. It's as simple as that.
And if you want the after-hours texting to stop, say so. He might protest, but at least it will open a dialogue and you guys can resolve the issue.
Good luck.
Well said, Cary. Communication is the key. Without it, assumptions are made that may or may not be true, and relationships can fall apart easily as a result.
As with SO MANY things, just ASK HIM !!
If he acts all shady and evasive THAT's when you start to give him the squinty eyes and wonder. Until then trust him to answer truthfully when you ask him things in a normal unaccusing way.