I have to agree with Mach on this one. Way too many words that are full of guilt. Yes they are how you feel, which is justified and understandable. You actually seem much less angry than I would expect.
Personally, I would also not address the Coach bag. You are allowed to buy stuff for yourself without having to explain that to anyone (unless of course it were to put you and your kids in major financial straits). I would simply say this is how much I need, this is how much you would contribute if you were here and leave it at that. You may have to consider separation in order to get the amount that you need and with two babies, well I don't think anyone would think less of you if you have to go that route.
"Acceptance doesn't mean resignation. It means understanding that something is what it is and there's got to be a way through it."--Michael J. Fox