One word: TIME.
I primarily play guitar, but I also play piano/keys and bass, and I've spent significant time with drum programming. When I picked up piano four years ago, after five years of exclusively playing guitar, I learned how to play by listening to other peoples' songs, learning how to play them by ear, and practicing what I'd learned constantly. As I became increasingly familiar with the instrument, I was able to start writing songs and patterns designed to challenge myself and increase my skills. After four years of playing, I still learn the same way.
I find playing multiple instruments refreshing rather than overwhelming because I do not try to play every instrument every day, nor do I try to increase my skill in my different instruments simultaneously. Instead, I focus on one at a time, either based on what I feel like experimenting with or based on which instrument I feel is lagging behind in terms of technical skill.
My greatest piece of advice for you, SantoUno, is to give yourself time with piano, bass, and drums before starting intense work on a specific project. Recording is very high-pressure, even when you're doing it at home. I needed a year or two of practice with the piano before I was able to start writing and recording piano/keys parts for my album The Places I Go (download and stream it for free at http://www.theplacesigo.net ). The more time you give yourself to get comfortable with your instruments, the more energy you will have free to spend on creative innovation rather than technical performance.