Can RSV cause a rash 2 weeks after a 10 month old gets out of the hospital?

Doubt it. I've treated thousands of cases over several decades and don't recall a rash associated with any of them.The germ selectively invades the airway tissue and is not present in the blood to any significant degree. Only blood invaders trigger a generalized rash.If a rash came up two weeks after hospitalization it is much more likely to represent something else.
I'm not sure... ...What your question is, precisely. If you're asking whether RSV (respiratory syncytial virus) can cause a rash, yes, any viral illness can be accompanied by a rash, although it's unusual with rsv. If you're saying the child was hospitalized for RSV 2 weeks ago, has recovered, and now has a rash, that rash would not be due to rsv. Something else is causing it, possibly a medication.