I don't feel like there is any "right" way to practice, or even play. When I play classical pieces (which I inevitibly hack to pieces) I will break up the LH and RH to get an idea of what I'm supposed to do. Then I go ahead and do what I can.
When I play jazz or pop I usually rely on the chord symbols to guide me on what notes to fill in on the RH for harmonic support and usually leave the LH to do block octaves on the root (or appropriate bass note) and put in appropriate flourishes in the bass part. But there are times I will concentrate on either hand to either work out the accompanying harmony in the RH, or understand just what the root movement is supposed to be in the LH. I recently have learned "Goodbye Pork Pie Hat" and had to do that to understand just how that piece moves in the bass...
I also started young on piano and then took a few years off and lost a lot of technique that I'll probably never get back completely. But that doesn't stop me - I am what I am, and I do what I can do. The key is to keep trying, and every once in a while something explosive comes out that reminds me that I once was a child prodigy of sorts. Now I'm a jack of all trades (piano, bass, guitar, trumpet) and try to use my entire experience in whatever instrument I happen to be playing at any given time.
So I think the key is just to keep practicing in whatever way seems to work, and strive to play a piece better each time you work on it. Expecting to play Chopin's "Heroic" to the level that could win a competition is unrealisitic for me, and I think a lot of people, especially those who once played seriously then stopped for an extended period of time. But it doesn't mean that you are destined to play cheesy arrangements of pop tunes from here on out. Just keep plugging, and find your own voice.