The outside wall of the house does not separate your property from hers. So it is not a "party wall" as defined by the Party Wall Act 1996.The wall between the 2 windows is where she is proposing to site the flue (bold white chalk mark), ie on a party wall...
See Party Wall Act explanatory booklet para 3, page 6.
The fact that you may or may not be building an extension is not really relevant. If the patio is your property, she is not allowed to discharge the products of combustion directly over your property. The flue has to be a minimum of 300mm from your boundary, i.e to the right of your patio fence. But she is then caught by the rules about distances from openings (300mm) and drainpipes (150mm).
There is nothing to stop her drilling a hole through the wall. The obvious solution is to use a plume management kit to raise the discharge point. Provided, of course, that the terminal does not infringe the regulations regarding distance from the windows upstairs!
See Approved Document J Pages 49 and 50.
The party wall act does cover this. It also includes boundary walls of which this is one.
I deal with the use of this act regulary. It is used more often for this than it is for the party wall.