Not to be a jerk, but it doesn't look like you're measuring that correctly. You need to measure the actual bolt circle- the pic looks like you're measuring off opposing bolts.
The 6x2 wheels in the PA link above are not only completely unsuitable for kart use, they're smaller than you think. The total diameter is 6", not the rim diameter.
The 4.10x3.50x4 are a little closer to reality in the size department, but complete crap and guaranteed to kill you or your kids.
If you find a good set of the 18x8.50x8 turf tires from a lawn tractor, you can get a pair of 8x7 trailer/ATV rims from PA with a dead common 4-on-4 bolt pattern that will work with them. PA also has a "drive flange" available that you can use to make hubs for that. The flange has a 4-on-4 stud pattern, and a bore that works with their weld-on hubs, so you's select the hub for your shaft size, put it on the flange, and weld together. I can supply SKU numbers if need be.
EDIT- If there's ANY chance you're mis-measuring those hubs like I suspect, the spread might be 4 1/2"- in which case you're dead lucky- that pattern is the common 5-bolt trailer pattern! Take a hub to PA and try it on their 5-bolt version on the 8x7 rim!