Well, there probably isn't anything that you can do about this situation - I think it is a limitation of the processing power of the iPad Mini 3. If you compare the iPad Mini 3 to the iPhone 6s you will find:
- iPad Mini 3 has an A7 processor, iPhone 6s has an A9 processor (two generations newer)
- Geekbench 64 bit score for iPad Mini 3 is 1385, versus 2506 for iPhone 6s (nearly twice as much processing power)
- iPad Mini 3 has 1 GB of ram, iPhone 6s has 2 GB of ram
The spec on video performance says that the iPhone 6s can process H.264 4k video at 30 fps, while the iPad Mini 3
should be capable of 1080p at 60 fps. Theoretically the iPad can do 1080p at 60 fps, but perhaps the videos that YouTube app offers up are not some other codec or container.
You can find specs on apple products easily at:
http://www.everymac.com/