We have issues with this, too, though my lads are closer in age (21 months apart). Like your DD, OP, and like my DS1 before him, my DS2 (now 12mo) doesn't sleep long without me (30 or so minutes, maybe, which is what his older brother did until he was probably 14mo or so). He's also a champion sleep fighter, even when slung or driven in the car for a while.
Anyhow... the main point of my post was to say that while slinging my DS2 is sometimes a good way for me to get him to sleep longer, a lot of times my older lad is really wanting me to put DS2 down so that DS1 can snuggle up to me (he still needs me in physical contact with him to fall asleep). I try explaining to DS1 that waking DS2 will mean taking attention away from DS1, but sometimes he replies "I want to wake [DS2] up."
: I think, though, that's a sign of a deeper need that he's trying to have met, and I'm still searching for the way to meet it while also caring for DS2.
My best hope of getting DS2 to sleep a while is to get him down, then get DS1 down (which is *much* easier said than done). If I can manage that before DS2 awakens, then I can often get DS2 back to sleep for a while. Now that DS2 is older, I lay him down in his brother's twin bed. If DS1 by some miracle allows himself to fall asleep for a nap (pardon the sarcasm -- it's been a long dry stretch of a nap strike), I lay him down in his bed, and the brothers sleep well together.
I realize this doesn't get at the heart of your post seeking help to stop your DS's behavior, and for that I think mommy2abigail's approach is a good one if it will speak to the need your DS is trying to have met.
At 4mo, your DD2 can't really be doing anything to annoy her older brother except existing, and neither can do much about that!
Hang in there.