The problem is not that Barberries attract ticks but that the deer eat everything but Barberries. Ticks sit at the tips of branches or grass, waving their arms; anything that brushes against them has a chance of picking them up. If the Barberries are the only thing left in the forest to sit on, then, yes, the Barberries will be infested with ticks.
I suspect all the plants in your yard have an equal chance of harbouring ticks if you aren't letting the deer eat everything else. Teach the kids to not plow through the bushes or tall grass in your yard. If you have a lawn, keep it mowed. Inspect your kids for ticks every day during tick season. Ticks hike around for awhile before digging in so shake out their clothes and give them a bath in the evening. The ticks will be under waist bands, in armpits and inner thighs and at hairlines. After ticks dig in, it takes about 36 hrs for the tick to take a "blood meal" and infect their host with Lyme Disease.