children imitate those around them. so, if a child does not pray, or rebels against any other fard, his parent should first spend at least some time looking in the mirror. should think about how much time he spends with his child, and what they do together.

because the hadith offers no immunity to the parent.

but when the parent has decided to raise that child among kuffar in America (classmates, neighbors, TV, etc.), then even if that parent is very good in observing the fard, that parent has surrounded his child with bad examples.

examples that not do not follow the fard, but which encourage the haram (dating, drugs, eating pork, drinking alcohol, etc).

such parents should be strict, and especially so with children who show any tendency to shirk what will be fard upon them after puberty.

children should be praying all five salat by the time they are 7. they should be physically disciplined if they fail to do so by age 10. and i did not make up that advice.

should the parent strike the child in anger? no, the Prophet, sull Allaho alayhi wa sallam, never encouraged anger.

he encouraged love for children, and he encouraged discipline. the hadith you have quoted does defend children. but it does not encourage lax parenting.