The mercy rule you talk about is in effect in most leagues that arent competitive usually art u12 age group - it goes out the window after that and our league has a 9-0 deficit as the mercy rule now whereby you can call the game off but carry on if you wish to do so but again I think that is pointless hence why I have a conversation with the manager and agree before the game starts that at 4 up you can add an extra player - I actually dont think losing to such a high profile side by the odd goal you talk about is a bad thing - it was competitive from the sound of things (Id guess you are used to winning most weeks hence the frustration???)
As I said in my earlier post the pressure to win comes from parents/coaches etc in my view and is very very wrong and shouldnt be the barometer at this age group you should be teaching them the importance of teamwork the ability to win and lose well, the importance of the role they have in the team and most importantly to have fun regardless of score which I am sure you do
Interestingly enough the number of Girls in particular who stop playing all sport in there early teems is alarming and a massive issue for all sport so Im all for the girls showing the boys how its done
https://www.bbc.co.uk/newsround/56360438