It is unfortunate that sometimes, things happen beyond our control, and these are moments to seek God's opinion through pastors, priests or people we know are older or have had such similar experiences.
Your situation is a complicated one because I can't figure out how the kids were cared for, when they were younger. Issues like this could be traced down to childhood experiences. Michael probably had a scar in his past which may or may not be your fault. Now is not the time to find who to blame, like Michael is trying to do: REFUSING TO TAKE RESPONSIBILITY.
Showing love is not enough, your issue seems like a case of misunderstanding between children and parents, which usually arose when there is deficiency in healthy or intimate communication (not mere chatting; which rarely involve trust). Michael probably does not understand nor trust you, so your love no matter what you do, means something else to him. He is yet to understand you are loving him.
Don't blame yourself, God knows and sees all your genuine efforts. Just focus on solving the problem, make Michael trust you enough to share his real problem with you, and try to reunite your family. The best solution is from GOD. PRAY, SEARCH THE BIBLE,GOD WILL HELP YOU GET THROUGH IT.
Please, don't be too hard on yourself, GOD sees all your genuine efforts and will see you through, don't hurt yourself unnecessarily when there is a way to find a solution. Intimate-trusting Communication with Michael (and the whole family about the issue, but first with Michael) and God will help get you through the pain. That is my suggestion. Good luck. Joan_Edwards