I'm a stepmum (and a stepchild) and I would have had our DSDs.
But it's easy for me to say that. Because DH is a good parent, who always involves me in decisions, never shirks his responsibilities, and doesn't treat me like an unpaid nanny.
The scenario above is highly unlikely to happen, because I simply cannot imagine him forgetting his children.
And if it did happen it would be a genuine accidental one-off fuck up, and of course I'd then step in to help with a proper mistake. (Not least because he'd ask me, not just have their mum turning up unexpectedly and bashing on my doors and ringing me).
HOWEVER, if I was married to shit dad (which it sounds like OPs ex is), then I wouldn't be nearly so accommodating.
For instance, if DH was forever expecting me to do HIS childcare, and didn't involve me in discussions, and didn't do enough parenting of our shared child etc etc - then I can quite imagine this being the last straw and refusing to come to the door and pick up the pieces again.
There is another thread where some CF dad has agreed to have the kids for the whole half term week, without telling his wife (stepmum), and is not booking any annual leave and expecting her to cancel all her plans and have the kids. On her first week of annual leave in AGES. Quite rightly, everyone is telling her to put her foot down and refuse to have them.
When mums (not stepmums) post in AIBU or relationships about their shit husbands refusing to pull their weight - they are told to refuse to pick up after them, to book a hotel for the weekend, and oftentimes to LTB.
Why is it that a mum is advised to book a hotel and force the husband to do childcare, but a stepmum cannot take similar steps to stop her husband taking the absolute piss.
I strongly suspect that her husband asked her and she already said no (otherwise why wouldn't she have come to the door), and he didn't tell OP assuming that SM would be forced to pick up the slack when they turned up.
TBH I think turning up when you knew your husband was at work was outrageous anyway. Why on Earth would you rock up at a woman's house unannounced expecting her to do your childcare?
At most, you should have texted her saying: "I'm really sorry, ExH has forgotten to have the kids, I've got a work shift, is there absolutely any way you can do me a MASSIVE FAVOUR and have them. I know it's not your responsibility but it would be such a help".
Perhaps if you treated her with a modicum of respect by sending something like the above she would have said yes. But it also would have given her the opportunity to decline if it didn't work for her without involving the kids.
You put them in a shitty situation and you put her in a shitty situation.
The ex is clearly the villain of the piece, but you've added to all the drama, with your entitlement to another woman's time.