One thing that should never happen is that the weight of the neck/guitar would be resting in your left hand. Even sitting, I prefer using a strap to hang the guitar off of my. You should be positioned so that your hands are free to do what they need to do and should not be supporting any of the guitar weight.
If you play with the guitar resting in your lap, make sure that the hip curve of the body rests on your left thigh and the butt end of the guitar touching the inner side of your other thigh. Th guitar should also be at a slight upward angle for the butt end to the headstock.
It sounds like you're holding the guitar while trying to fret notes and that's impossible and will drive you nuts if true. I think most kits come with a strap so you may want to try working with that.