Thanks for writing to Just Answer.
The first thing to do when someone presents you with possibly hurtful information is to consider the source.
Does this person have anything to gain by telling you your partner may be looking outside the relationship? If not, I would take what they said seriously. But what you do with the information is what's important--not whether it's "hearsay" (that only counts in a court of law).
You said that the relationship is in turmoil, so it could possibly be true. But the biggest point is that you now know just how much turmoil/ trouble your relationship is in.
Are you going to use the information in an argument with your partner, or are you going to use it to spur you on to work even harder to end the turmoil?
When people are unhappy, they often "look around" to see what their options are. That doesn't mean that your mate is cheating. Looking around can also be a way to build their self-esteem back up when turmoil at home is making them feel badly. Having a flirtation is dangerous, but can make the person feel desirable again.
If you want to save this relationship, try bringing it up something like this: " I know that you've been unhappy, and might have even started looking for someone else, but I love you and want to fix what's broken in our relationship. Do you want to keep working at it too?"
If your mate denies looking around, don't get into a big " well, so and so said...." There is nothing to gain from that type of argument. Focus on going forward and fixing.
I wish you all the best as you try to sort this out with your mate.