I'm from a big family with lots of different personalities. I don't know if DH is the eldest as I can relate to the driven thing.
You will have know for a while that this brother isn't going to be getting you a White Company bath set, or anything meaningful, yet you still went to town and got him nice stuff. You've changed that now, but I can imagine if your in laws are all opening nice presents and BIL gets a tin of celebrations, that is going to cause an argument.
He obviously needed to get home after a night out, thus the £20, couldn't one of you picked him up or is he really far away? When it comes to siblings I have to say YABU to decide if DH helps him or not.
I've got a younger sibling who decided for several years even with debts they weren't going to work, which meant from board to food to debts we all helped out where we could. I would say sibling has always been the favourite, they have their issues, you could say it's annoying they only text at birthdays, at Christmas we were told we'd be getting nothing as they can't afford to. Then saw the massive stack of presents for each SC who all wear designer gear. If they want help they'll time it so they know you can help, I've given them the last of my money in the past. When it's the other way around you get Crazy demands like I'll help you out, take you to Dr's but it'll be £20. You're left quite gobsmacked as I taught them how to drive in my car, before they could drive and even after we'd give them lifts, one was literally 10 to midnight NYE. I said well can we see in NY together, no I need to get going now, kind of thing.
DH will be well aware of their sibling, at the same time DH might feel guilty as they've always worked hard and done well, something that doesn't come naturally to BIL. So he helps to compensate this. I'm guessing even if by text DH will have arranged to help possibly.
You've got to decide do you want BIL to impact your relationship, do you want frequent words about BIL asking for help? Or do you want to just leave it to DH as long as DH isn't making you short as a family.
I've been in the same situation most of my adult life, whoever I'm with saying I'm crazy to help any of my siblings. But I've worked hard and am successful or was successful, so even with friends, I've given money as I don't see the point in lending as often you'll never see it back. I remember splitting up from a guy who had roughly calculated how much a friend owed as I gave them a loan too, but didn't overly expect to see it back. The guy decided half of what she owed me was due to him, even though he lived a cushy lifestyle off my back.
So after all that waffling unfortunately YABU as it's an IL. Also you really need to think about picking your fights. Do you really want to have a day of DH & yourself not talking over £20 or over your BIL?
YANBU to be annoyed, but to take the phone and end the conversation I can see why DH was annoyed. To me it's just not worth the hassle.