First I think it is awesome that you are going to do speed dating, that will definitely help with all of this. As far as the set up goes at your place there are a few ways you could do it, but you want to make sure they are together so that they are always working on their relationship. By this I mean separate pens next to each other. I used to have a free-range bunny that I then bonded with a new bun, and it was hard on all of us when we had to lock her up, but it is only for a short time. Eventually the tantrums stop and your bunnies will start to focus on each other for attention and entertainment.
As far as at your parents’ place goes, that is a little tricky. See if there is another bedroom to use if your bedroom is too small and set it up like you would at your place. If not, ask your parents if they have any suggestions for where to do this. You may even have to ask a friend for temporary housing for the buns so as to avoid any potential problems with the cat. You can get rabbits and cats to get along, but you don’t need that on top of bonding your buns. On a funny side note, bunnies usually dominate cats.
I would check out these resources on bonding for more details
http://www.thebunnyguru.com/care-guide/bunny-bonding/
rabbit.org (search for bonding)
Let us know how it goes and if you have any other questions!
Good luck!