The only way he will stop "forgetting" (which is BS) is if you stop relenting and putting your plans off to do his job.

yes you made plans yes, you matter.  But you can easily change your plan to the next day or so and go with DH for his injection.  Have to give him a change.  If you don’t want to be involved with SS, you must put some effort in not being involved.  You should be happy that he understands this. Lot of people will not, and want the Happy Family and can’t see how you don’t want that with SK ????

I’ll say this much - your family affairs trump your DH not wanting to cart his own kid to a Dr. appt. This is a life lesson, on several levels. 1) In the future your DH gives you at least 48-72 hour advance notice, so you can plan your schedule accordingly, and 2) It’s never too early to teach children manners and patience, when it comes to having to wait for their parent in a medical office setting. 

I would have NOT changed my plans because he “forgot.”

If your DH can not manage HIS son, perhaps he could drop him off with his MOM. The child is not your responsibility, and you have plans that you informed him about. How does he know the others you are meeting can accommodate a change...and why should they even have to?

Kids can go to a doctor's office.  I don't consider that reason enough for you to change your plans.  Now, if it was a job interview?  Yeah.. that would be more in line with a situation that you helping him out with the kids would be worthwhile and necessary.

In my house, DH and I have the understanding that I will not be left alone with SS ever.  SS almost 9 is a liar and will do/say anything to stay in BM's good graces.  I will not allow myself to be vulnerable to that.  I am willing to be alone with SD for short periods (i.e. car rides), but that's it. I cook meals for everyone, but if they don't want what I cook, that's between him and the skids.  I don't discipline.  I don't do their laundry.  And how DH manages those things isn't my responsibility.  DH respects my limits and understands why they're set where they are.

If your DH had been asking you to drive him to the doctor, I think that you wouldn't have thought twice about about dropping your plans, even with the short notice.  That would have been about taking care of him, and you're OK with doing that.  The issue you're having is that he wants you to support him by providing care for your skids, even though he knows that's not your job AND he waited until the last possible minute so that you would be put into the position of feeling like you *have* to help him care for the skids.

Ultimately, I don't think that your DH respects you or the limits you set, and I'm not sure he's willing to learn how.  Each time you post, I get the feeling that he just wants what he wants and to hell with anyone standing in his way (you).  That's a terrible place to be.

Your Dh has OSS too, where was OSS that he wasn't going to need watched also?

I would have no problems telling my DH 'no, sorry I have plans and you knew I had plans' . Your DH should be able to let two children the ages of your skids to tag along and sit in the waiting/reception area. These are not little boys. He could have also called BM and asked if she perhaps was going to be home and he could swing the kids by her home for the short period of time. If his kids were halfway 'normal' (no burning down the kitchen, opening cans with knives and who knows what else) he could even leave two children of this age alone or asked the neighbor to check on them. 

IMO it isn't simply supporting his parenting efforts, or occasionally 'helping' him that your DH wants. He can't handle his kids, he doesn't know how to parent his kids and he'd like very much if you would just do it for him. 

You've pulled back from doing his parenting for him and removed yourself from engaging in his poor attempts to parent them himself .... don't let him guilt you. 

I think you drew the correct line. Your DH doesn't take your needs and limits seriously as it is; had you relented and watched the skid, it would have just shown your DH that he can run roughshod over you and you'll allow it no matter what you've told him.  Actions speak louder than words.  Maybe now he'll remember to give you some notice when he needs a skid-related favor.

It boils down to respect and value.
You schedule things to accommodate others  - plan ahead.

Your DH shows you a lack of respect and de-values what you do by demanding you change things to accommodate him and his children.
What he needs and the arrangements of his children are far more important than what you need.
I draw a hard line at that kind of disrespect.

I went through this too.  DH and I, once when he "called me out" on my disengagement we had a great argument.  He was sick and tired of my lack of involvement - well, DH, then you give me some decision making power and we'll see how involved I want to be.  No more undermining, no more "expecting" me to do things...it didn't really stop.  When he backed off was when I physically actually stopped doing it.  That's how he learned.

I was very firm, and no yelling, leave anger out of it. 

DH, I made these plans a week ago and it's been on the calendar.  My plans involve more than just me (or maybe it's something for you that you cannot do any other time) but other people.  If you knew you needed me to take care of SS for a couple hours, it cannot be last minute and I will not change plans I already have.  If this was a true emergency, I would help.  But SS can accompany you to the doctor's appointment.  I would appreciate notice if you need help with something, and then we can make a decision together.

He just can't take the responsibility can he?  You have done absolutly the right thing, unless you model adult behaviour to him, he will always fall back to little boy mode if you let him.

I did not connect who it was.  NO go see your family, let DH handle his kids