Not all rims are measured the same. It'd be 559, not 599, for a 26" tire in any case. Compare inside widths, measure them yourself to be sure if they're 18 or 22 (22 could be exterior). In either case a 2.1 tire shouldn't be a problem (I use 2.4s on a 17mm interior width rim without any problems, altho it's outside "recommendation"). Width of a rim doesn't necessarily indicate strength of a particular rim, depends on other factors.
Rims of the same ERD use the same spokes, but check out your current rims before you try swapping.
Mostly you shouldn't worry so much and go riding.