How your boyfriend is with his son is characterological, not situational. You are describing his character, not his condition. You say he is inconsistent, insensitive to your needs, dismissive of your attempts to help, competitive, and fearful of the child’s mother. Do you really want to be with someone who consistently creates a condition where you are resentful and alienating?
If you are going to stay in the relationship then a meeting with a family therapist is essential. If your boyfriend says he isn’t interested in changing, then you may want to consider moving on.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral