I, too, like the compromise in which you take care of the two-year-old while daughter in law gets herself to and from the appointment, BUT, I can see this backfiring big time.
The “why can’t you just take me since you have to come here to get two-year-old, anyway. It’s not even that much out of your way! Plus, I need to go by the pharmacy to get my vitamins, and I need to pick up milk, and you are going to have to bring her back to the house anyway, and, and, and, but, but, but....” and before you know it, you are driving her everywhere again, and you are de facto assuming responsibility for this new baby.
If she misses this appointment for lack of planning, she will just have to make another next week and find a way to get to it. This will force her to step out of her comfort zone and figure out ways to help herself, and face up to the reality of her situation.
She is a very dependent personality, and you are kinda acting as her parent, spouse, and fail-safe to keep her from facing reality (and making it so that she can continue to produce babies she can’t take care of with men who won’t support them).
I know it’s a very difficult situation, and in reality, I would want to help, too. But, it’s better if you don’t.