Your not alone. I think this describes the typical day for most people. It's hard to find the time to learn new stuff and keep your skills sharp.
You need to make more time in your day or use the time you have more effectively. Having little time means you probably won't be able to sit down and read a book for any amount of time so your best option may to be to find audio books, podcasts or tutorial videos you can listen so whilst traveling or performing other work that does not require to much concentration.
Just a few tips...
If your serious it's worth considering to invest in your own future with one of these services.
I've learnt several server side and client side programming languages over the years whilst at the same time running my own small software company - it can be done you just need to be passionate enough and you'll do whatever it takes to find the time.
I hope something here helps you get the ball rolling. Best of luck for now,