I think the player is being a bit unreasonable here. You warned them that the consequences of taking a rest by themselves would be being excluded from the gameplay, they agreed and then got upset when exactly that happened. Did they give you any example of how they wanted to be included? It looks like they're trying to eat the cake and have it too. You can't include them if they have deliberately and willingly just excluded themselves.
FWIW I think you already were generous letting them complete the rest while stuck in the bag and carried around.
I wouldn't let the players take a short rest by themselves anymore. Unless the whole party wants to take a rest together, no one does. This is one of the house rules that I use at my tables, precisely to avoid situations like what happens here where a player wants the PC to stay behind to rest and then complains about being excluded. It also helps keep the party together and prevents situations like splitting the party in half because 2 want to rest and the other 2 want to continue and then half of the party stumbles across something that was meant for all of them to face and gets wiped out.
If you're running a module that you think incentivises the party to split I've find it useful to provide them some means to keep contact between the groups or/and work out some rules to allow players whose PCs aren't taking part in the scene to still contribute and stay engaged.
If a PC is low on health and a player doesn't want to continue they can either persuade everyone to stop and rest, ask someone to heal them or just proceed carefully and hang out at the back with some ranged weapon. It's not so easy for a character to die in 5E anyway, at 2hp they're still a long way from dying. If the player still refuses to play while presented with this reasoning then I think it's some sort of out of game problem and requires out of game handling to get to the bottom and solve.