Outside taps should always be fed directly from the main. No connection with the hot water system, DTC.
Is the AGA connected to an immersion cylinder?
If so, is it a "Direct" system ( old-fashioned direct connection to the cylinder where the hot water runs through the AGA, through the cylinder, and then to the taps.) (One roof tank only - usually results in "brown" water occasionally)
Or... is it an "Indirect" system ( AGA heats water from its own separate roof tank then transfers the heat indirectly to the contents of the cylinder via a heat exchanger coil within the cylinder.
I bet you didn't understand a word of that, DTC. Can't blame you. Difficult to explain. A plumber would identify the system with one glance ;o)