Learn English – “can hardly” vs. “there’s no way”

I feel that on the literal surface, the two phrases have very similar meanings since they both mean doing something with the other person/people. However, "play with each other" has a strong sexual connotation, because when you play with something, the thing you play with is your toy. So, when you play with someone, there are two meanings: playing together with someone, or using a person as a plaything. When you put those two meanings together you get the obvious sexual connotation.

Thus, playing together avoids any hint of impropriety.

Note: other similar phrases:

Playing by myself: one person, playing.

Playing with myself: masturbation.

Of course, all of this rests on the fact that "playing" has a connotation (among adults) of sexual activity (or it's an outright euphemism). So you can reach the same connotation even among adults if you say "let's play together"... people have to be clear ahead of time what is meant by play.

They are not always interchangeable.

I would say that someone who scored 60 on a test for which 60 was the lowest possible passing grade barely passed the test, but not hardly passed the test.

I would say of someone I thought unsuitable to be, for example, a high school teacher, that "He's hardly the type of person who should be a high school teacher", but not "He's barely the type of person who...".

That's American English. I don't know about other varieties.