Well one point you have going for you is that she hasn't kicked you to the curb already. Lots of women, particularly when they have children to raise, hit a point where if you are not going to be able to provide for them, then they are damn sure going to find someone who will. And that is not romantic, it's mercenary - but there are a lot of parts of life that mercenaries win all the time and romantics always lose at. Kids make that kind of choice an overwhelming necessity.
Look, do you love her? Really? If you do, and if you know damn well that this is not going to work out in the long run, by what right do you have to hold her to it (thus not letting her move on, find the love she needs, wants and desires) until you feel OK with walking out that door to live your life? Is she to suffer through all the stuff till you get all your ducks in a row, and then 'hasta la vista Baby'? That sounds even more mercenary to my ears.
Let me say this, and I know everyone is going to hate it, but true is true. No one forced you to have kids. No one stood there with a gun to your head and said "impregnate this woman." And, so long as you did it without duress - no matter how wrong the reason was at the time - you have an absolute moral obligation to support those kids.* EVEN IF IT MEANS YOU DON'T TRANSITION. Sure, its all fine to say "it's my life" but it's not anymore. You have moral obligations that you are NOT free to pass off to the next sucker while you go out and 'discover' yourself. (And hey, you have a Master's Degree, you must have thought some parts of this through already.)
Yeah, I know, you're going to pay for the rest of your life for something that only took a few minutes. While I'm not crying for you, I will give you a couple of names of people I know who are doing what amounts to life without parole for a couple of bad minutes in their life too. At least you can still go out to the store.
You owe it to her, and to your kids, to make a damn decision, and if you don't stick with it, at least don't stick them with it either.
* - Because if they show up on some welefare line that I have to pay for I'm going to go all Dickens on them and ask:
'Are there no prisons?"
'Plenty of prisons,' said the gentleman, laying down the pen again.
'And the Union workhouses.' demanded Scrooge. 'Are they still in operation?'
'Both very busy, sir.'
'Oh. I was afraid, from what you said at first, that something had occurred to stop them in their useful course,' said Scrooge. 'I'm very glad to hear it.'
...I can't afford to make idle people merry. I help to support the establishments I have mentioned-they cost enough; and those who are badly off must go there.'
'Many can't go there; and many would rather die.'
'If they would rather die,' said Scrooge, 'they had better do it, and decrease the surplus population."
---from A Christmas Carol by Charles Dickens
YOUR KIDS, Your responsibility, even at the cost of what makes you happy. Even at the cost of 'being who you should be.' At any cost.