I don’t know, but I think if you can just give them a list of her daily diet and ask that they not experiment with anything not on the list, it should be OK.
Tell them she will be stressed out with you gone, so any change of diet could be really serious, so it’s best to keep her routines as much the same as normal as possible.

I just searched it and found a couple of good websites. From what I’ve read, mulberry leaves are not only safe to give to your rabbit but a study that was done showed that mulberry leaves can also help lower your bunny’s cholesterol. ( Sounds like a Cheerios commercial, doesn’t it? )

Here are the websites if you want to check em out:

http://earthhome.tripod.com/saferab.html

http://health.wikinut.com/The-Mulberry-Leaf/26ta9bc9/

http://rabbittalk.com/safe-plants-for-rabbits-list-t55.html

On the topic of you leaving your bunny with your family while you’re on vacation, I agree with RabbitPam. If you tell your family that experimenting while you’re away might upset her, I’m sure they’ll listen. Then you can enjoy your vacation without worry! ( Even though I’m sure you’ll still be counting down the days until you’ll be able to see your rabbit again. )

 Welcome and thank you Harmonee.   I also did some checking and can’t find anything “toxic” about it. so far  Here is a list by  a rescue group which includes mulberry in the non-toxic list. http://www.3bunnies.org/non_toxic_plants.htm  I also checked out the “etherbun” forum that is strictly about health and many sources there claimed it to be safe. (with the exception of if it’s been treated with pesticides and watch for any fungal growths).  I would have to check with my own rabbit-savvy experts to feel 100% confident, but I will put this on my list of questions to ask. 

I also triple ditto Pam and Harmonee about telling your parents to only feed what’s on the diet list while you are away.  As even if something is safe, you don’t want to add anything new to a diet when you are not able to supervise your bunnies digestive reaction.  (as even some safe things can cause gi upset in some bunnies). 

Have a wonderful vacation!