And I don't want to sound or look like a whiny little puppy dog, which I would have had I asked any time over the summer.
You've hit the nail on the head -- the ONE thing you cannot do is whine. It sounds to me like you've been doing the right thing here -- giving her space -- but that it's still painful, you're hurting, the pain is not going away as fast as you thought it would, and you're starting to lose your resolve.
Don't do it!
The irony here is that the more you act as though you need her back, the weaker and more whiny you look, and the more unattractive. The more you fail to respect her saying "no" to you now, the more you remind her of the other times when you were (in her mind) disrespectful of her needs.
On the other hand, the better you look as a loving father, respectful new partner, and overall healthy guy, the better you look to others AND to her.
IMHO, you have been doing the right thing -- what you need to do now is MORE of it, not less.
It's counter-intuitive, but the best thing you can do is to focus elsewhere. How can you be a better and more loving father to your kids -- overall and during this upheaval? What would you be doing to improve yourself if you believed that you'd be looking for another partner someday? What self-improvement for your own sake (health, fitness, education, etc.) have you been putting off?
Even if you've had counseling with the wife, you might seriously consider going on your own to figure out WHY you a) didn't appreciate what you had until it was too late b) picked the wrong person in the first place c) didn't notice the warning signs, d) didn't have the tools to fix what was wrong, etc. etc. (I'm making this up -- fill in the blanks with whatever YOU think you might have done differently.)
At best, your ex will come to see you with new eyes and think you're worth another try. (Highly unlikely, but stranger things have happened.) At worst, you'll be happier with yourself, more in tune with who you are, more in touch with your kids, and more likely to succeed with a new person once you're ready.
One last comment -- if you think your parents are heartless and insensitive, there's even MORE reason to focus on your kids and what's happening to them right now -- you do NOT want a repeat performance in your generation.
Whatever you do, good luck with it. I know its painful, but you DO live through it, even if it doesn't feel like it at the time.