This is the real problem. We have a 20 year marriage, two kids, a nice house, sterling credit. You know, the American Dream. How do you uproot all of that? Is it right to do so just because I'm unhappy in my marriage? On the one hand, I think, maybe this is as good as it gets. On the other, I think I'd rather be broke and hunting for food with someone who cared about me than safe and dry with someone who does not. You only get one life. There's no reset button. But is it right of me to upset hers? She seems to have no complaint. Is it right of me to upset the kids' lives? I go over this stuff in my head all the time.
So on the one hand I'd sacrifice everything and anything for my wife and children.
On the other hand you aren't constrained by my beliefs about children and family.
So speaking from a worldly perspective, "But is it right of me to upset her [life]?... Is it right of me to upset the kids' lives?" is self-sacrifice to a damaging degree.
It tells me your depression really isn't resolved - martyrdom is not a positive, healthy trait. What does your therapist say about these thoughts and feelings? Are they, objectively speaking, reasonable, or do they proceed from a faulty brain chemistry?
Does your therapist agree with you that your wife doesn't care for/about you, or is it possible that this, too, is still being filtered through either the mental illness itself, or the side effects of the medication?
You can ask yourself or us these questions until the end of time, but I think your therapist is probably the best person to get an objective assessment from. We don't have enough information and you are compromised.
Even though you're better, it's possible that through some additional manipulation of your medication you have additional headroom to improve your happiness.
That said, as others have doubtless pointed out, your wife and children need you to do what's right for you, just as much as what's right for them. If things are objectively as bad as you state - and they may well be, I hope you understand I'm not trying to undermine your experience, just point you toward a solid foundation on which to base your claims - but if things are that bad, then you must set an example for them on how to resolve the issue without destroying things. Some fathers/husbands leave and do a lot of damage in doing so. Some never leave and everyone else learns that life is meant to be a joyless sacrifice.
Handled well, though, such a break will provide an opportunity for everyone to learn how to adapt and change to the improvement of everyone's life. Not to say it has no downsides, every break involves heartache (lifelong) and pain, but put on the balance it may be worth it given the increase in total happiness and opportunities for joy.
Also, I'm lazy and haven't read through the thread recently, sorry if this has already been asked and answered: is it possible that your wife also suffers from depression? There may be reasons she can't/doesn't show the affection and love you need that aren't by choice.