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All you need to do if you have that problem is to move the tire on the rim 45 degrees (of course you could lose that "pro" look of the tire label being in line with the Presta valve); retest the tire if it still wobbles move 45 degrees again etc until the wobble is reduced. Most of the time I can get any wobble to be all but eliminated. Also as another poster mentioned the position of the computer magnet will have a major effect and should be opposite the valve. Cheap tires and tubes will also cause a problem with wobble due to imperfect manufacturing; I've actually seen tires with bulges where the rubber was thicker then in other areas! but that doesn't effect a kids bike that will never go above 15mph.

Does in inbalance tire have an effect on your riding...depends on how fast your going to go. The kind of balance is called harmonic, and this harmonic vibration is similar to a car tire which is why a car tire will only vibrate between a narrow range of speed like 45 to 55, but I've seen car tires start ot vibrate as low as 35 but will only last in about a 10mph window. So on a bike unless the wobble is very severe (like the one I had when I absentmindly once placed the computer mag near the valve) your not going to feel much if anything until you exceed about 30mph. When I did the computer mag gaff I thought something was wrong with my bike it vibrated so badly, but this didn't get noticed until about 25 to 30mph.