Glob, It's certainly something to explore in counseling.
I am an extrovert and have always derived my energy from other people. H is an introvert and I can honestly say (nowadays) that we balance each other out. He has taught me how to enjoy being alone and doing quiet activities and I've taught him how to enjoy (tolerate?, lol) interests outside our home.
My point is, there's nothing wrong with being an extrovert but if you feel like you CAN'T be alone, that's another story. Have you always felt like this, or is it due to the loss of OW? Is the depression over that situation causing it to be worse? My advice is to do whatcha gotta do to get thru your current depression. Bearing in mind, of course, that your wife and children are not responsible for ridding you of this pain. But if you need to be around people right now, then do it. If you need counseling right now, call someone. Same with short-term meds. Or working out tirelessly. Or whatever!
I agree with you about pushing past it. It will be hard but it will be no more or less hard than your wife pushing past her own I am a Rock comfort zone, kwim? Hopefully you will both grow and learn how to be good spouses to each other.