Apart from contributing to this preference to believe what dsd says when she runs her mum down. Which mum does visa versa.
I know what has led dsd to know she can play them off against each other but not sure how to make her stop. He knows this one is dsd's doing and has done the "talk to the hand" thing but mum can't seem to accept that dsd has caused this and so come the angry calls and texts. DH is now very wise to what dsd is up to and how her claims about what mum does or says are largely untrue.
He needs to make much more of an effort to disengage. It doesn't matter that the mum does the same as he does. Can you not see that the tit for tat is what this whole stupid thing consists of? He does/ she does/ he says/ she says -- and on and on and on..
It doesn't matter who 'caused' this. That language belongs in the playground.
It is up to the alleged adults here to grow up and start behaving themselves, and showing the DSD how adults behave. She has terribly poor models on all sides right now. She needs at least one set of adults in her life to behave like grown ups.
How to make her stop playing them against each other is for your DH to stop allowing himself to be played. You can only be played by a 15 yo if you allow it. It takes two to make a running fight over something stupid like school lunches and how they are paid for. It takes two to contribute to the dynamic of a 15 year old playing two alleged adults against each other. Two immature dickheads.
It doesn't matter what she says about the packed lunches, or what the mum believes. It doesn't matter that the mum thinks your H is feckless or tight. It doesn't matter that the DSD 'caused' this.
Stop wishing mum was different. She isn't. You and DH have to get imaginative, and most of all you have to disengage from the relationship with the mum. You can only control what happens in your own home, in your own heads and your own hearts.
This is not a fight between your H and the mum unless your H chooses to make it so. What he needs to do is be a better parent to the DSD, and he can do this by growing up, putting his relationship with the DSD first and not using it in a guerrilla war against his ex.
Your H is a dick because he refuses to do something simple that would make the mother's efforts with the DD easier, and chooses to do something else. Why won't he just do it?
It would solve the problem of the mum being on your case if he just did as asked. Would it kill him to do this? What point of principle is he trying to prove here?
Put the money in the school lunch account and stop pandering to the DSD and her efforts to create drama. Find other ways to give her the attention she craves. You need to figure out why DSD is behaving as she is, and accept that her dad is playing a big role here, and figure out how to stop the merry go round. He needs to show her that dad is good for more than money, and stop feeling sorry for himself and playing his 'I'm the Victim of the Wicked Ex' script in his head.
I would suggest giving a reasonable amount of pocket money, taking the school lunch cost out of it.
What do the two of them do together at visitation time?
What interests do they share?
What activities does the DSD do where the DH can cheer her on?