Hi Elz!
How exciting! Lops are just the absolute cutest!
Definitely separate them! I personally spent $175 on my doe to get her fixed last year, which also included the extra pain medication I needed when after the spay, she didn’t eat for approximately 24 hours. Keep calling around. I know at one point I had 3 rabbits (two does, one buck) spayed and neutered and they gave us a “package deal” to get them done, so maybe see if they will with your two? If you are only fixing one, the doe is definitely better to get fixed just due to the health reasons. They develop reproductive cancers VERY easily after the age of two. However, it’d be beneficial to each one to get them fixed.
I have three cats at home, and when I am in college I have 1 cat, 3 other rabbits, and a VERY large golden retriever. She LOVES cats, actually. My cats generally get along with her too. The best thing that has worked for me is a 4ftx4ft doggie play pen. All in all I believe I spent $65 for the cage on amazon, and it is a white plastic (which makes it a tad prettier than a wire cage) with removable panels to make whatever size you want. It gives her so much room to run around, and on days where I am studying and super busy to the point where I’m not home to let her out, she isn’t really mad about it at all because there is so much room in her pen. This pen has a swinging door on one side of it as well, so when I want to let her out (which is usually open when I am home anyway), it is easy to do so. This way is also very easy to get her back in. I have trained her with freeze dried fruits, to which she knows the sound of the bag shaking means she is getting a treat! This is much better than when she was first very small and not trained, and better for our relationship as well.
I have her on a carpet, and over the carpet I use 2 yards of fleece fabric. It works perfectly to cover the whole span of the cage and is washable, changeable, also very fun for you and even your kids (I love changing the fleece patterns for holidays and seasons) You can also tie the edge of the fabric to the bottom of the cage bar, if need be, to keep bun from digging and bringing up the blanket (which I have never had a problem with really). I also have a tile in one corner of the cage just in case she gets too hot and a hide for her to go in.
As for litter box, just keep putting their poops/pee (by soaking it up with a tissue) and place it in the box. When Bindi was a baby, I had another litter box outside her cage as well (just be careful because I had problems with my roommate’s cat peeing in my outside the cage box, which I would have to empty and clean every time he used. Bye to all the money I had to spend replacing the carefresh until I finally rigged a system so he couldn’t get in while I was not around. ?). Also, spaying Bindi made a HUGE difference in her litter box habits!