Totally agree with Kaluki .... it isn't being horrid to DSS for the sake of it, it's a needs must situation. Purpleroses also had some good ideas.
I can see that the prospect of sharing with a toddler might be onerous for many teenagers who might worry about lack of privacy and the potential for a younger child not quite understanding that they mustn't touch certain things - either because they're precious, or because they're dangerous. But that will improve in time and can be relatively easily overcome with, say, lockable storage and/or high shelving. In reality, and in regards to privacy, just how much time will a 13 year old be spending in that room anyway if contact is usually only EOW ? Obviously, it can be explained to him that if he needs quiet time for homework, DS will be kept out of the way, or somewhere else to do homework will be provided. Similarly, I can't really see that if he wants an hour or two to himself during the day on his own that he wouldn't be able to get it ..... IME, most 3 year olds may pop in and out of their rooms but they don't usually spend lengthy periods in there on their own when awake as they want to be with other people - and most parents would want them where they can keep an eye on them!
Don't know if room is big enough, but maybe a screen of some sort could create the illusion of defined areas ? Or a room divider/bookcase type thing ?
This is the sort of conundrum which many families must make the best of - sadly not everyone can afford 1 room per child. As NADM said, if he's part of the family, he should be treated as such - i.e. whatever solution you come up with, if it was the same thing you'd do if the kids were all yours, then that's fine and nothing to feel "guilty" about. I disagree totally with making visiting kids into "guests" and treating them with the same kind of consideration you'd show an old aunt down for the weekend - that sort of thing, where particular children are singled out for special consideration (usually prompted by fear of contact stopping if they aren't pandered to) is very quickly picked up by the other kids who have to like or lump stuff if they protest. Surely the best way of making a non resident child feel like a house is a home is to treat them just as you would anyone else living there permanently ?