We used to pull our kids at that age behind a 14' aluminum boat with a 10 hp motor. In reality, it was slow as heck and you couldn't even swing them outside the wake, but they loved it. I had to drive them around on that thing for hours! It's what eventually led us to get a 'real' boat.
If they are wearing vests and are comfortable in the water, it can be as mild and as safe as you make it. Put mom on the tube with each of them so she can see how they're doing. Personally, I would not get up to planing speed until the kids are a bit older or until they have had a few slow-speed wipeouts (actually, at slow speed, I'm not sure you can consider it a wipeout...). When they are read, straight-line tubing at planing speeds will seem pretty exhilarating, and when they're even older, you can start swinging them outside the wake. Our kids were pretty good at telling us when they were ready for more excitement.
What is your wife's concern? Injury? That the kids will get scared?