High bar and low bar kip should be very close to identical, the only difference being that the hips are piked for a glide on low bar, and they stay extended on high bar. Either way, the key is to hit an extended hollow shape as the front swing stalls out; from there, the two skills are identical.
If you can do a low bar kip but not a high bar kip, it is almost certainly because you're tapping through the bottom of the swing and therefor bringing the feet up to the bar too early.
As for at-home drills, strength. Specifically, hollow body holds (with the hips as extended as possible), V-ups, pull-ups, and my favorite strength drill for kips: toucans.
To do a toucan, pull to an inverted tuck with your ankles touching the front of the bar. While keeping your ankles lightly in contact with the bar the whole time, lower straighten the legs as you lower the hips to end up in a toe-touch position, then return to the inverted tuck, keeping the ankles in contact with the bar the whole time. If you really want to go the extra mile, you can bump up the intensity by lowering from toe touch to L-hang in the middle of the toucan, then return to toe-touch, and then lift back up to inverted tuck; doing that with good form takes more strength than the kip, though.
