You may not know this, but YouTube on your PC or laptop can actually be controlled from any smartphone, without installing any apps or linking the two over a network. All you need to do is use YouTube TV.
As Redditor circasurviv3 points out, it's a simple process. Just go to www.youtube.com/tv on your computer and press "S" to bring up the search menu. You'll get a prompt to pair your PC with your smartphone by going to www.youtube.com/pair from your handset and typing the code provided. And that's it — you're controlling YouTube on your PC from your smartphone.
Sure, you can install an app like YouTube Remote or elaborately control your whole PC with your Android phone, but this is a no-fuss, no-installation way that works with any computer and any phone, not just your own.