I was 10 when my younger brother was born, and while I of course loved him very much, he drove me crazy. 10-12 I thought were always awkward years because you're growing out of the kid stuff, but you're not at the teen stage yet, plus right before and during puberty is always a tough time. (Not trying to pry but maybe his recent behavior is related to that "magical" time approaching.) Anyway, my brother used to get into my things a lot too, and it was the perceived violation of privacy and personal space that I really didn't like. If you don't already, I would suggest buying some sort of lock or childproof knob cover for his room and the bathroom. They have plastic pieces that can snap on over the knob that the little one won't be able to open, but you guys and DS could by squeezing it. That could possibly reduce some of the aggressive behavior, but I would also make it crystal clear that any mean behavior will absolutely not be tolerated. Set rules and consequences and stand by them. There's no way I'd personally allow electronics if there are behavior issues, but I'm also a mean mom that has yet to buy my 8 yo any electronic device.
Next, if your DD is keeping him awake at night, I'd look into earplugs, noise cancelling headphones, a white noise machine, or something to help reduce the sounds. If he's not getting enough sleep, that could be contributing to his crankiness.
It sounds like between homeschooling, never really taking time alone for yourself, and your DH not always being around due to work, etc, that your DS spends almost every second with you. Frankly, it sounds like YOU need a break. Rather than getting a sitter every other week for your DD so you have more time with DS, I'd consider having a sitter stay with both of them (or your DH, but if he won't, do the sitter) at least once a month so you have some time to yourself. You seem a bit overwhelmed and something I've had to learn is you have to take time for yourself or you won't have as much energy to devote to your kids. It might also be good for your DS to have that little bit of time away from you. I know it's tough when your best friend moves, but if there's any way he could spend more time with other kids his age (through the homeschool groups, going to the park, kids activities at the library, kids bowling league, etc), that might help as well.
In regards to your trip, I personally wouldn't leave DD with a babysitter for that many days. Yes, the trip will be different, but he has to learn to accept that things will be different with a younger sibling and that family trips are for the family to spend time together. He's had several trips that were devoted solely to him (whereas his sister hasn't and may never have one where she's the focus of everything) and it's not really fair for his sister to be left behind, just like it wouldn't be fair for him to be left behind for half of the vacation.
Do you have photos of him at Disney when he was young? Bring those out and point out the joy on his face and tell him about memories you have of taking him when he was so young. Explain to him that his sister is going to be so in awe of everything around her and he gets to be a part of that magic. (Because even though she has been before, there's a huge difference between 6 months and a year and how the little ones see and react to the park.) Emphasize that he gets to help "create" the magic for her by showing her all the things he loves at the parks. He might like being allowed to plan a day at the parks so he can "introduce" her to all of the cool things he enjoys. Let him know that being a big brother comes with the responsibility of looking out for his sister, but also teaching her about the fun stuff. With responsibility also comes benefits, like maybe staying up a little later while his sister goes to bed, but those benefits have to be earned.
Good luck with everything.
I will definitely go with DS and see what tactics I can implement here at home though. Fortunately we are not dealing with Asperger's, as I realize how challenging must have been for you all. This is a big adjustment, I am an only child; so I try to think of how I would have felt in these situations. Again thank you for your reply 
