Tricia Ruth would be best to give you specifics as to "why" & good examples of where to look. You've got a few things you seem to want to work on. LH patterns, rhythm, improv, hand independence & technique.
All of this will come in time as you play. Try not to think about it so much. When you get stuck in your head creativity suffers & you get all hung up. Been down that road many times! I'm a frequent flier!
Here's a few things to check out. Don't overwhelm yourself with all the info! Try a few things to get comfortable with, & expand.
There are so many things you can try for LH patterns. 1-5-1, Fifths (1-5), alberti bass, rocking the 1 w/3 & 5. off the top of my head I'd check out more in Lovin Leadsheets, Riffing Pro, Arranging for Solo Piano, In the Vault: Chords & Comping, Improvising In Any Key, Techniques & Drills, Tricky Fingers, Rhythm Station, Flowing Piano, The Club Mix, although that comes out in pieces. Good Luck & Have Fun!