I don't think this will fix it, or is an answer
but if you haven't already you could try to check in your Settings for 'App Associations'
and make sure that Dolphin Web Browser is selected as your [default]preferred YouTube Link choice
You could also check in the classic browser and make sure that Flash is turned on in there, even though you aren't utilizing that browser. Might as well make sure that it is not somehow 'closing the gate' for Dolphin (It shouldn't
work this way - they are independent of eachother, but I guess it is worth a try).
Does connecting via WiFi vs. your mobile network provider make any difference in your situation?