Which Personal Pronoun To Use?

Was having a long drawn out discussion with some of my colleague lunch (but had no idea who came up with this question initially). But still not quite sure if the outcome of our discussion is conclusive. Now we have the following two sentences:

(1) We don't play with him. (2) He has ...

So we wanted to join the above sentences using the relative pronoun "who" (as opposed to "whom"). This is concluded after some deliberations as well.

We don't play with (he / him) who has ...

Now the question is which personal pronoun to use? "he" or "him"? But in the first place, can we join the two sentences in this way?

After doing some research, I've found the following:

1. "He" is a subjective personal pronoun. This means that the pronoun is acting as a subject of the sentence.
2. "Him" is an objective personal pronoun. This means that the pronoun is acting as an object of a verb, compound verb or preposition.
3. In sentence (1), "him" is the object of the preposition "with" (is this correct?)
4. "He" is the subject of sentence (2).

So we got a problem when we join the two sentences. Is the person a subject or an object? Or maybe we can join the two sentences in this way:

He has ... , so we don't play with him.

Can someone enlighten me?