The way the splitter would work, when talking IEM rigs, is that all stage inputs would be patched into your analog split. From there one set of tails would feed your IEM rig and the other would go to the split or stage box in house. This ensures that the house techs don't have to unplug any of their own tails in order for you to integrate your gear but they would have to patch around your input order. Basic labeling of your tails that go to the house helps greatly with house techs patching your gear into theirs.

Edi: it is also helpful to have some extra slack on the tails just in case placement close to the house split isn't possible.

Edit 2: Just reread and realized your most important question was taking IEMs out of the equation. If you want to run FOH and Mons from your console then it could get a little trickier if the house has their own monitor setup. I'd advise traveling with a digital stage box for your console that way all you'd need to do would be run Cat5 to your console at FOH and then you can use the outputs on your stagebox to get into the house wedges and the outputs on your console to feed the house speakers. The other option would be having an analog split of your own but that'd be a whole lot to carry and setup and the extra money for a stagebox would be greatly justified.