I'm not sure what you are asking by asking if it is 'common'. I would say something is common if I say it (say) once a week. I've never ever said that sentence, and even if you had used something other than the american word 'mom', I might have said it at most a couple of times in my life. But that's because I've probably never had a reason to say it. But yes, it is probably natural for an American to say.

Hi Shima, Usually, “S1 had a frank discussion with S2” is used by a third person observing from outside, or by the person with more power who started the discussion. It’s not really something that the person who gets talked at would say. So I can imagine someone’s mom saying to someone else (maybe a friend) “I had a frank discussion with [child’s name] last night”. And usually the person mentions the topic: “I had a frank discussion with Jennifer last night about her cutting class.”