OP it's so awful when your second one arrives - beautiful and wonderful etc but also AWFUL! It's normal to feel pulled every way, and like you're being a crap mum to both kids. I cried so much for my baby, who wasn't getting anything like the focus and attention I was ablew to give my eldest, and for my poor eldest, who was used to being the apple of my eye for nearly 4 years, suddenly having to be told no, not yet, wait, get down what felt like ALL THE TIME. Also, the bizarre feeling of leaving an apparently tiny child to go into hospital and give birth, then coming home to a HUGE enormous monster of a child who seems to have doubled in size, volume and general obstreperousness overnight compared to the tiny vulnerable newborn you brought home with you. It's awful!
BUT it doesn't have anything to do with their gender, and it won't last. Honestly, your son is little. He's being aggressive and stroppy not because he's a boy but because he's a toddler. My eldest DD loved the IDEA of a baby sister, and made all the right noises about looking after her etc. This lasted about half a day, and then she became incredibly possessive of me, heartbroken, and rough with the baby. Because the idea and the reality are two very different things.
So yes, protect your little one as much as you can; hammer on 'kind hands', and praise him extravagantly for every positive interaction, even if he's not as 'gentle' as you might wish - learn to tell the difference between excessive enthusiasm and poor motor control vs actual intent; accept the fact he will probably sometimes get a pinch in, just as you will sometimes scratch her with a rough nail by mistake, or cut her with the nail scissors, or or twist her little arm getting her onesie off - she won't be badly hurt and it won't traumatise her, as long as you're attentive enough to head it off at the pass; NEVER leave them alone together, even for a second, until this phase is past.
But it will pass! I have to say your concerns about him still hitting her/attacking her when they're 13/11 sounds crazy to me and makes me think your brother's behaviour must have been very extreme/unusual - I can't think of any children I know who would actually hit/hurt their sibling or playmates routinely past the toddler age. I had big sisters, 2 and 4 years older, and though we would argue we would never 'fight' as in physical violence past about 4/6 years old. Is this something that routinely happens with boys? I would have thought by that age and in that era, they would at least have had it firmly drummed into them that boys don't hit girls.
Anyway, don't borrow trouble. He's two, she's 5 days old - history is not 'repeating itself', their story has barely begun! Keep on protecting her, but don't turn against him. Use words a lot - he may not yet be very verbal (boys sometimes develop more slowly) so help him with his feelings: "It's very hard to share mummy when you're used to having me all to yourself. I can see you're feeling angry/upset/frustrated (whatever it may be); but we have to use kind hands to [baby]; if you want to kick, shall we go outside and kick the ball against the wall? If you want to hit, you can hit this cushion. when you're ready to use kind hands, we'd love you to come and cuddle with us." I know it sounds naff and scripted but I actually found having this sort of stuff 'lined up' in my head stopped me being reactive and shouting or blaming/labelling in a way that sets up and cements conflict ("why do you always do x?").
And definitely when dad gets home, offload baby and give him 20-30 mins of really high quality focus. It doesn't have to be ages, but he has to be reminded he is still hugely special to you, not just a distraction from/threat to the baby. It feels crap on baby, but honestly they get used to what they get, and you are still giving her a huge amount of focus and input. There's a reason, I think, that firstborns are often quite intense and high needs, vs secondborns being quite independent and chilled - they get used to what they get and respond accordingly! Eventually your babies will even out, their size and their capabilities and their needs - especially with two so close in age. Give it time, remember that it will n all likelihood pass, and that you are not your parents, and are not going to allow a situation to develop where your youngest is being consistently hurt by your eldest. Let go of the trauma and the trigger.
In other news, my youngest (2) pushed my eldest (6) off the top bunk of their bunkbed yesterday, so I know whereof I speak (no-one badly hurt!). She was told off on the spot and banned from going on the top bunk anymore, tiny tantrum, forced apology, all done. But later on, completely unprompted, she came and found her big sister, hugged her and apologised. Because she's two, she sometimes actus up because she's two, but she absolutely loves her sister, who loves her too. Watching their relationship with each other grow, watching them learn to play with each other and compromise, has been the absolute joy of my life and my favourite thing about having children, more even than my relationships with each of them. I wish I'd known how beautiful it would be, when I was spending about 6 months crying every day that I was letting everybody down and wishing for both their sakes I'd never had a second!