Dan, I like shooting anything from landscapes to close-ups of statues and clocks on bell towers. So I like the whole range. I have three lenses for my Canon 5D Mark II DSLR: a 17-40mm, a 24-105mm, and a 70-200mm (with 1.4X extender).
FYI, a "10-20mm lens" isn't going to give you the same view on every camera. Your camera may also have a "crop factor" - meaning, your camera can "see" only a portion of the lens. My 5D does not have a crop factor - it is a full-sensor camera. So when I put my 24-105mm lens on it, I'm seeing the full 24mm when zoomed out. But if I put that same lens on a camera with a crop (like a Canon 7D - crop factor of 1.6X), that 24mm is effectively cropped or zoomed to 38.4mm. (But the 105mm is also multiplied by 1.6 - so it's effectively 168mm.)
So is my 24-105mm wide enough for someone's Canon DSLR? As you can see - depends on the camera! Someone with a 7D might want Canon's 10-20mm EF-S mount wide-angle zoom (which actually won't work on a full-frame DSLR like my 5D). That would give them, effectively, 16mm-32mm compared to my camera - about as wide as my 17-40mm lens is on my camera.
So what's wide enough? Assuming you have a crop camera, your 18-130mm is probably wide enough for me. I basically lived with something that wide on my last trip to Italy. I've taken my my wide 17-40mm and a bag with several other lenses to Italy a few times, but in May, I visited Italy (and France and Slovenia) with a new Lumix DMC-FZ1000 "bridge camera," which has an (effective) 24-400mm zoom built into it (and a big low-noise sensor). (My 24mm probably being about as wide as your 18mm - with the crop factor taken into account.) A few times on my recent trip, I did miss the wider lens from my DSLR - but I lived without it - and was very happy instead to have a much lighter camera to deal with. On the other hand, this was the first time I have traveled with something as tight as 400mm zoom, and I REALLY used that a lot! This is the big benefit of having such a variable zoom lens: not needing to drag a bag of heavy lenses around to get a variety of wide and tight shots with a single lens, without getting a sore shoulder.
How much in Italy would you miss not having the new wide zoom you are contemplating? Probably a few times. I think you'll mostly use your existing zoom lens and switch in the wide once very rarely, when you just can't step back to get the wider shot you want. You'll just have to decide what kind of pictures you really want vs. how much more weight you want to lug around!
Sorry I can't give you a definitive "buy the lens!" answer - but I hope that helps!