Thank you for you email. I understand your concern for your son.
I am pleased that your son is seeing a child psychologist and he must definitely continue with the therapy.
As you have correctly stated your son is angry and jealous and is in a lot of pain, that is why he's acting out.The best way to help him is to adapt your parenting techniques to meet his needs. He's asking for more alone time and attention and you can give it to him by arranging dates with him. Let him plan something fun for you and him to do alone such as have lunch together. Focus on listening to him and letting him take the lead when you're out together. Make sure you are having fun together. He should also plan a date with his dad.
Ask his psychologist to help you with the best words and ways in which you can manage him, such as not raising your voice to him when he becomes defensive, but rather try to acknowledge his feelings. Allowing him to have more of a say in things that affect him.
While we strive to love our children equally, we may treat them differently and they are aware of this perceiving themselves as not being loved as much as their siblings. Focus all your efforts on identifying what your son needs emotionally and trying to give it to him. Tell him you love him and that he is very precious to you. Allow him to plan a big birthday party for his next birthday and keep your attention on him during this time ensuring that he feels his party was the same as his sister's.
Good luck! Let me know how you are all doing.