I'm afraid there is only one interpretation for that sentence:
"I, who is now at school, think that he will come to school today."
It's because of the verb 来る as you said, for one reason. But 来る・行く is not the whole reason.
"I think my son will probably go to school today."
This sentence still have only one interpretation:
"The speaker thinks that he will go to school today."
In order to express, "He thinks that he will go to school today," it should be written as the following:
or something like that.
I would change something a little in order to avoid the ambiguity which you mentioned in this question.
If "彼" has a mental disorder and he doesn't know what he is going to do next, いyet, the subject of "彼は今日学校に行くと思います" is not "he" but someone else.
"彼は今日学校に行くと思っています” means "He thinks that he will go to school today."
In order to express your interpretation, use the present progressive tense in this context.