I did this last year. With two camera systems, four AF lenses among them, and a dozen Minolta lenses, I was paralyzed with too many choices. I got the X-E1 and 27mm pancake shortly before the trip, and ended up taking the the Fuji/27 and a Samsung NX with 30mm f/2 pancake. They are practically the same size, and I wanted to do a compare/contrast. Over a several day trip, each day I picked one camera to carry, and each fit nicely in the pocket of my shorts. Both cameras had 'normal' lenses and worked well for a variety of conditions.
All of which is to say... I'd take the X100T; The GR is pretty wide at 28mm eq., the LX100 is probably bulkier than the X100T with that big square-edged lens, and the 18-55 is going to be in your way all day. The 35mm eq. lens on the X100T should be wide enough to get some context in your shots, while still allowing you to get portraits of your family without wide-angle distortion. It's also compact enough to not bug you...
Have a fun trip!