Dontask ..... would your H agree to counselling about this ? You could sell it to him as an opportunity for you both to air your views but FWIW, I think you have every right to feel hurt and upset. There's the lying, the double standards (eg. subbing EX but refusing to spend similar amounts on your home) and his apparently willing assumption of responsibility for someone who has since remarried (albeit now widowed).
I'm not surprised you feel bottom of the heap. As others have said, generosity to adult children is fine - if you can afford it, and if it's agreed jointly - but supporting his ex wife (above and beyond any legal obligation, eg. the terms of a previous court order) isn't something he has to do and whilst this might be explained away as simple generosity it doesn't add up when his attitude to you - his current (and hopefully last) wife is so different. No question about it, you should be his 1st priority. I obviously don't know the circumstances of his divorce, but is there any possibility he still feels residual guilt over how things ended (and the money is a way of assuaging that ?) or, even after all these years and the fact they're adults, does he believe that if he didn't help her out, his ex would stir up trouble between him and his children ? If so, these are the sorts of issues that counselling might help with.
To my mind, unless, as I said earlier, he had a court ordered obligation to her, his responsibility to her definitely ended when she remarried (if not before, when the kids became adults). Most court orders of that ilk usually stipulate that spousal maintenance ends on remarriage anyway. Once remarried, the ex and her new husband would surely, like most couples, have discussed their finances - currently and in the future - made wills, took out life insurance etc ..... as indeed they seem to have done so far as you know, and the fact she was married before would have become an irrelevance so far as continuing financial support was concerned. Having remarried, whether she was widowed or not, I simply don't understand why so many respondents seem to believe that because her husband died, responsibility for her now seems to have been passed back to her first husband ?!? That's certainly not the case legally, but nor do I think it the case morally either. Both parties are supposed to have moved on, and if ex wife and her new husband didn't have the sense to put their financial affairs in order, why does that become her ex husban's problem ?
Regardless then of them once being married to each other, if she asked him for money - as a friend or acquaintance - which is all she is now, that request (or requests) should have been discussed with Dontask if there was even the slightest possibility her husband was considering them. If she was in genuine trouble, and if the money could be afforded, perhaps a one off gesture wouldn't be out of the question ...... but regular top-ups are grossly unfair. From what the OP has said, it doesn't sound like this woman has had terrible luck, or genuine emergencies, but is inclined to overspend and/or mismanage her money and sees Dontask's husband as her own private cashpoint. She's taking the piss, but then of course HE is enabling her, and effectively encouraging her to do that if he never puts his foot down.
The emotional side of this - about DH demonstrating who's 1st in his life is bad enough, but purely practically, I absolutely cannot get my head round any scenario where a man prefers to have his wife of 11 years (so no falsh in the pan) go without whilst "helping" (being a mug) out his ex-wife .... and one who was remarried to boot. I do think the ex wife is behaving very badly .... especially if she, and their children, are aware that these goings on are supposed to be a "secret" and are obviously going along with that ..... but the main problem here is Dontask's husband and she needs - somegow - to sort him out. The ex wife & kids could be outrageously demanding, but it wouldn't actually matter if Dontask's husband dealt with them realistically, honestly and fairly. That means keeping Dontask in the loop at all times and agreeing - jointly - what was and wasn't affordable/acceptable.