I have been divorced since my son was 4. He is now 11 and I am remarried to a wonderful man who is a very involved stepfather. My ex is also remarried and although over the years we have all had our disagreements we have NEVER, any of us, let it escalate like that or acted out in front of our son. Your husband's ex was completely out of line in that respect.
I also agree with your husband that there is NO reason for the sister to be take out of school too, unless they are twins joined at the hip! That makes no sense to me. Since it is supposed to be your husband's day for the girls,it sounds like possibly the ex did it on purpose, just to throw a wrench into the system.
Now- if there was no absolute reason the appointment had to be on a Wednesday (that was the only day her doc was available or something) then changing the appointments to a different day should be no big deal- particularly if your husband is offering to take his daughter to them if needed.
On the other hand- if your husband's ex-wife was expected to be the one taking the girl to the doctor, you can't complain about when she makes the appointment, IMO.
In our family, whoever makes the appointment (and it is always me, because my ex generally won't be bothered) makes it for when it is convenient to their work schedule, etc.
If your husband did not want the appointments to be made on 'his' visitation day, he should have brought that up immediately with his ex, OR offered to take the afternoon off work and take his daughter himself. Always remembering that the key, most important thing is that the little girl gets to the doctor when for the treatments she needs.
I am not saying that the ex was not purposefully trying to be difficult- it sounds like she was. But- your husband has to be proactive too- if he didn't like the appointment situation, he has to offer to take care of it himself, and not just complain about it and wait until it is a done deal.
I'm not trying to be mean- but I have been caught too many times, when my ex just took no interest in something or didn't get it done on time and I was the one scrambling to get the camp physical or whatever scheduled and then he didn't like what day was the last appointment left, etc. It is a pain- but working EVERYTHING out in advance is key to doing this kind of thing successfully IME.
If it is a big enough deal to complain about, it is a big enough deal to DO something proactive to take care of it and avoid complications!
I think you should suggest meeting with a mediator and your husband and the ex. You can describe the scene at the office to the mediator (they have seen and heard everything under the sun, so don't feel embarrassed or weird about this) and talk about your sd's reaction- poor little girl to be caught in that situation!
Having an uninvolved 3rd party may help your husband's ex see the error of her ways- or at least realize that her behavior made HER look very bad. (Be forewarned that my ex is always extremely well-behaved at the mediator's- totally reasonable and responsible sounding, etc. But mediatos almost never fall for this, lol)
If you go to a judge for any kind of changes to the parenting agreement, the first thing you are likely to get asked is if you have sought mediation on the issue, so you may as well be the ones to suggest it now, which makes you look good and again, will reflect very badly on the ex if she refuses. My ex and I always pay half each when we do a mediation- its cheaper than an attorney at any rate.
At the very least, the mediator will help you to draw up a set of 'rules' both sides agree to use when similar situations come up in the future. I know this sounds childish and even ridiculous when you are talking about grown adults- but I can't tell you how many times having the mediator's 'rules' has kept things from escalating for us. The mediator will also write it up as a legal addendum to your parenting agreement that can be filed with the court- so if your husband's ex ignores it in the future, he has some actual legal backup on his side.
Good luck- these things are always sticky and his ex does sound like a pill- I can't believe she acted that way in front of her own poor kids! But remember- just blaming her for being mean or a ***ch is not going to get anything done- you and your husband MUST be proactive about things, or it won't help.