I have mixed ideas on this.
You say you're having difficulty expressing authority.
Expressing authority... everyone knows you are officially in charge right, and that you do have the "power" to take away privileges or whatever, right? IMO you don't have to express it at all: it's a given. Once you build your confidence, even a direct challenge won't shake you. It's why people who really do know something don't bother arguing with someone who doesn't.

I absolutely agree with pointing to the "rule" and making sure when someone pushes the limit that the admonition isn't coming because of you, but because of the rule. (This is taught to parents so they sit down and make rules with their children and then it's the rule the child broke, not the parent's waivering wish.) But along with the "rule" there needs to be a resulting "punishment" (Sorry, I know there are more professional words but I'm in a pain flare.)

So at that point, once all know the rule and the result of breaking that rule, it's out of your hands and you are not the ogre---it was their choice to break the rule, and the rule includes the punishment. (Oh I hate that word!)

Don't go too fast. It's so common to want to implement everything right now because it's "needed" but as you said, this is something they haven't had in a while (or ever?) so go much more slowly than you first planned. Make a timeline of slow progress and then you'll feel less frustration at the slowness?

And don't forget the overall goal: keeping the patients from digressing during the weekend between their sessions etc. I could see how just having new rules implemented would tend to make them uncomfortable and perhaps invalidated (like they aren't behaving and now need you to tell them how to act?)

Plus, they might be accustomed to having free time as well... and while structured days are good for most, they also need free time...be sure they plan that into the weekend too. But even freetime requires we all continue good self care---all humans need to do that, so they need to know that as well.

Rely upon the therapists etc to give you feedback as to what is working and what isn't... I'm sure their patients will give them an earful! Plus, with an actual timeline of when to implement each part of plan, you can have it at staff conference if necessary.

Now breathe. Keep the patients alive and you've succeeded the most.