Poor Mrs M. My heart bleeds for her. NOT. The EA should have explained to her that gazundering someone will probably not endear them to you hugely and that one of the risks is that they will tell you to gfy and walk away from the whole deal.
Can they even re-market the other house based on your acceptance or not of their shitty offer?!! If there were people falling over themselves for it the EA probably would have engineered some gazumping situation already to push the price up or been on to you about upping your offer in the interim... They are so full of BS. 
Whether they can re-market or not, that goes to show the kind of EA they are - personally I would sack them off by going down to the office all pregnant and mental and losing my shit in the middle of the shop in front of other customers. 
If you are feeling a bit more restrained than I clearly am, then I think it is a brilliant idea to speak to your vendor independently of the EA, explain the situation to them and see what they say - with a bit of luck they will be fed up with the EA and shout at them too.
Then you can sell your house through the other EA, get the house you want and piss old Agent F all in one swoop.