Severe Bluetooth Connectivity Issues - OS X Yosemite+El Capitan
There is a lot of pain, but you have all the tools you need to isolate the issue:


Install 10.9 on an external drive. 
Install 10.10 on an external drive. 
Install 10.11 on an external drive. 


It is important to get a totally clean install of the three items above. You can then use a notebook to write down the exact times and OS when Bluetooth if flakey. If it's really the software drivers, you will have statistical evidence of that after 10 to 20 data points. The down side of this, troubleshooting like this is expensive time-wise and we don't ever get that time back. 

I hate to throw hardware at an issue, but wired devices or upgrading to Apple's newer hardware have helped in areas where I had clients with noisy 2.4 Ghz environments. The new hardware is Bluetooth low energy and superior to the old devices in terms of resilience and the amount of time to link back up when they inevitably disconnect. As a bonus, they work over USB in the case of the new "magic" keyboard and trackpad devices. Other third party options also exist with transmitters that don't depend on the Bluetooth stack. 

Make a "budget" for your troubleshooting effort and buy a solution that you could return if it doesn't solve our issue. Since it happens so often, you should be able to know with Apple’s 14 day return window if the new hardware will solve your pain. (And if it's cheaper once you put a $ value on your time to troubleshoot the issue further.)


Reset Mac OS X Bluetooth service?


Also, this answer to the above question has some critical information on using the debug menu to factory reset things. You might try each of these (writing down what you do and when - leaving a little time between each option) to see if a reset helps. The logging and diagnostic report will also help if you need to engage Apple support to troubleshoot the issue. Sometimes looking at the logs has helped me identify a failure.

Best of luck - I'm curious what you find out.