Beside myself with anger

How much of your anger is about the relationship you share with your partner?
Do you have a legal agreement about your cohabitation, who inherits what if the other should die suddenly, how you'd share property and goods if you separated? This may sound mercenary but ridiculously in 2019, cohabiting partners have few legal rights.
The link with your wish to influence your partners will is connected to those questions. Planning for the future is part of a life long relationship. I expect given you've been living together for 18 years, that's what you are committed to. Making a will is part of that. On that basis, I do feel its something to discuss jointly. Those discussions may highlight the communication problems feeding your anger.

Your partner needs to be the one to call a halt to this.
Your problem is with him and you have no business in trying to dictate his will.

Ugh! I don't blame you for being angry! Or your partner either! His DD and XW must seem like a constant drain!

IDK if they're purposely trying to make things harder for your and his relationship or if they're just irresponsible w/ money. Or while XW may be a troublemaker, his DD may simply feel her father should help her if/when she needs it. And, right or wrong, he may feel he should to. Are you sure you wouldn't feel the same way if she were your DD?

Regardless, I understand your impulse to demand that he leave her out of his will. But I don't think you should act on it. Too much chance of her taking you and her brother to court to fight it. Besides, your partner may see this as a matter of your not liking his DD (clearly, you don't), and that won't go over well. It will just cause tension between you and him and, perhaps, even a rift.

I hope you have your own separate money that you keep in an individual account so partner can reach into that for his DD.

(I'm not suggesting in any way that the breakup was his fault.)

He may have some deep hidden guilt for the marriage breakup. However unfair or unreasonable guilt has a way of sneaking in. Like the way guilt nags at a person who's cared and looked after a loved one unstintingly when the lived one dies. Perhaps some counselling may help your partner stand up to them?

It doesn't seem very fair on his son either unless he gives him money too.