Can't get Mr. House to allie with BoS? There were 2 dialogue options that tried to persuade him to accept BoS as an allie but both were turned down outright. So the only way to continue The House always wins quest is to destroy BoS?

There is no way to proceed with Mr House while maintaining the lives of the BoS bunker, the options are there to allow you to attempt to convince Mr House and - as you have spotted - fail. In order to progress you must erase the BoS by one example: destroy the bunker.

Reno