"(1)The little child is lonely; he would be happier if he had someone
that he can play with."

I'm trying to understand what "can" or "could" has something to do with a
subjunctive mood in this sentence because all I see here is that word
"would" only determines a subjunctive mood. The only reason why it is not
clear and people got stocked on words "can" and "could" is because in this
sentence essential phrase " he would be happier " stands before "if."  I'm
not sure if there is any standard form of sentences exists for each rule,
but it is more comfortable for me to see a subjunctive mood here if you will
rephrase this sentence a little bit: "The little child is lonely; if he had
someone to play with, he would be happier." But I definitely won't use
"that" for the relative clause. Also I want to say that "can" and "could" in
this sentence don't sound wrong because we got used to listen to many errors
in modern spoken English that we are just simply having hard time to define
what is wrong and what is right. When millions of people speak in an
improper way it is kind of hard to say that everyone of them is wrong.
Respectfully yours, Aram