The canon is a better system for tracking action like your daughter running around. The kit lens is a good one, but much slower then the K-x in auto focusing. If you upgraded to the 15-85mm IS USM it would be have no problems keeping up with your daughter. But the k-x is not the far off the canon with their AF.
With the canon, if you need all the video abilities for HD, the T2i is the better of the two when shooting HD. But if HD is not as important, the t1i will let you save some money, and it just as good as the t2i in the photography aspect.
The ef 50mm 1.8 is a good lens for the price, but it is slow to autofocus. Though it is a bright lens at 1.8, when in a low light environment, the lens have AF issues, and hunts allot. But it a good lens to start out with prime lens shooting.
I shoot the T1i and K-x and both are very good camera, but good for action shooting and low light shooting. If you do what to go into prime lenses, "fix focus ranges", the canon offers more lenses for that purpose.