I sometimes make characters and monsters to use their Reaction (if they still have it) to perform things like releasing enemies or fleeing in terror. I actually got the idea from an existing spell in 5th edition, Dissonant Whispers (pg. 234 PHB):

The target must make a Wisdom saving throw. On a failed save, it takes 3d6 psychic damage and must immediately use its reaction, if available, to move as far as its speed allows away from you.

Normally you're not able to use your reaction to move, but this spell shows that it's not impossible to be forced to do unusual things with your reaction via magic.

In the case of turn undead, I would possibly have the skeletons which have already acted use their Reaction to move and the rest move normally on their turn. It can be a tricky balance.

You have to be careful and decide ahead of time what a creature does with its actual turn when it comes round. Otherwise, you could make spells more powerful than you intend by having creatures run twice as far away or less powerful by creatures still getting an action on their next turn for example.

Not Necessarily

Vampire's Charm

The specifics of Vampire's Charm are more impactful than a standard charm:

The charmed target regards the vampire as a trusted friend to be heeded and protected. Although the target isn't under the vampire's control, it takes the vampire's requests or actions in the most favorable way it can...

In this case, the charm increases from Charm Person's friendly acquaintance to trusted friend to be heeded and protected. Agency should still not be fully removed from the character, but this is a much stronger effect and should treat the interactions with the Vampire differently. You wouldn't necessarily go against all your beliefs, but you are going to protect the vampire and listen to it more than you would just a friendly acquaintance.

Combine this with the mechanics of the Charmed Condition and you also gain advantage on ability checks to interact socially.

A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects.

The charmer has advantage on any ability check to interact socially with the creature.

Does advantage translate to anything more?

The big question is whether or not you can persuade someone to do something against their beliefs. Mechanically, the charmed target is still under their own control, they just view the charmer as a trusted friend and therefore will listen to them more than they normally would. Whether or not that means you can take their agency away is going to be dependent on the DM and table.

How I'd rule

At my table, I would not allow one creature to persuade another to do something that is against their beliefs, unless they could come up with an argument that makes that action feel like it goes with their beliefs when it really doesn't. But that's going to be on a case by case basis and a very tricky effect to pull off. If a party member can't persuade another party member to do something against their beliefs (which they shouldn't), then neither can someone casting Charm. Vampire's Charm is still going to have them protect the Vampire, but not necessarily allow the Vampire to dictate actions (even with a successful Persuasion Check.) To do that, you need something like Dominate Person.

In your specific case, Protecting the vampire is your major concern. Allowing him to have a trial rather than summary execution would likely fall under that. But I could also see the Vampire trying to persuade that you that he wouldn't get a fair trial. It doesn't mean you'd help him escape given your beliefs, but it would mean you'd try to make sure it was a fair trial.