Do you have my children?
My girls are close together in age as well, and as soon as dd2 was old enough to be interested in toys, dd1 started getting upset every time dd2 began playing. And just like your older son, she seemed incapable of sharing the way other kids were being expected to share. At playdates, she was regularly put into tears by the other girls who came over demanding that she share the game she had going.
It was extreme, in our case. DD2 was getting old enough to need toys to play with that weren't baby toys. I did try the "if it's on the floor" and dd1 started putting every toy in a huge bag and hauling it around with her. We had to hide or get rid of every large bag in the house to keep this fairly reasonable. We also tried the bedroom to no avail. DD1 felt banished.
Her intensity forced me to reconsider the status quo advice for getting kids to share. From our playdate experiences, I also came to the conclusion that this can wind up being "forced sharing" and that is just as selfish and keeping all the toys to yourself. OK, maybe in the Laura Ingalls universe, where a doll, a chipped cup, and a little wooden man constituted all your toys, I might say "yes, share!", but every house at playdates including mine was awash with toys. These girls were coming over to my then-3yo daughter and saying "you have to share" and then hovering until dd was in tears and ready not only to go home but never to return. It really upset me. She had a good story going with the animals-- ones we had chosen with some good conversation at the beginning, saying that she did have to share so to only pick a few, she couldn't pick all the animals and that should be good. (She sometimes did pick all, knowing that she was supposed to share when asked). It didn't help much, either with the inevitable demands for sharing (the whole game, not just a few animals of dd's choosing or some other intermediate solution) and dd's heartfelt tears.
The house rules ended up being that you didn't have to share one particular game if you were playing with it. My girls were both told they needed to find another game after asking if they could take a turn--no hovering. For a time, I had certain groupings of toys that were or weren't allowed to be piled onto their game (to prevent the hoarding that had been happening. This was a temporary rule.)
They did take turns, though not always well. They did learn to find other games to play while waiting, a skill I felt was a really good one (kids see another kid play with a toy, and even though it's been sitting, ignored, in plain sight, suddenly it's the IT toy!)
I must admit, that it really was last ditch effort to maintain sanity, but I did learn a few good things along the way (like disliking kids hovering, demanding a part of the game). It was not ideal. I would have loved to have my girls be eager to let each other in to an established game. They did learn to play better, once dd2 was about 2.5 especially. They are excellent at taking turns, and they never are that kid standing and hovering over a toy (they were not allowed to in any setting-- something that no other child seemed capable of).
Unfortunately, they are still not great at sharing in the standard way, which I think is something of a handicap socially, but then I consider what I started with, the intensity of what I was dealing with, and I am satisfied. At 6 and 8, we still have these conversations, for sure. Kinda frustrating, for sure, but I have to remind myself of where I started, and I let it go.