What is the ruling on not praying in congregation—not all the time—due to the inability to go to the mosque, for fear that a two-year-old child might cause harm to the worshippers, knowing that he cries and screams if he does not go out with his father?

Congregational prayer is obligatory unless there is an excuse, and what is mentioned in the question is not an excuse that permits abandoning it, as you can distract the child with his mother or someone else. However, if the child is genuinely harmed by crying, then you may pray at home while striving to find a trick to get out of this situation.