BM complaints

[Apple]

Looking for some insight. 

Since school started BM has come up with complaint after complaint about things at our house.  My belief is she's trying to make a case to end the Thursday overnights (we've been doing them for about 4 years, kids are 12 and 9 - we started them as soon as they lived close enough to make it feasible).  BM recently lost a motion to end Thursday overnights at our house. 

Most of BM's issues come to DH as "the girls complained that..."  The most recent complaint is they're not getting enough to eat for breakfast and are "starving" at school.  I'm the one that feeds them, I know they're getting enough to eat.  Their breakfasts are very high in protein and will keep them full for hours.  BM comes at DH with emails saying things like "this must be fixed ASAP."  Usually she has about half the information.

Can DH ignore these emails?  If we were to ever end up back in court, DH does not want to appear not to care, but BM is trying to pick fights.  He usually will respond that he'll speak to the girls about the issue but BM will continue to insist we're doing something wrong and it must be addressed.    

On the same line, DH and I want do what we can to make sure the girls aren't giving BM fuel for the fire.  We in no way want to suggest they can't be open with mom about dad's house, but we want them to come to DH with issues at DH's house.  DH is very close to the kids and they will answer questions (not that we interrogate them in anyway) when asked but don't seem to what to bring things up.  I believe BM is digging for issues after they've been with us.  Suggestions for how to address this with the kids without making the issue worse? 

[ocean]

Pick and choose your battles. Do not respond to every single email, especially if it is about the same thing. The breakfast one ignore. Have him talk to kid about breakfast without you "hey, I got an email from mom that you are hungry at school, what is going on?". It may be they are used to different breakfast and they really are hungry or it may be ex. Address it. Do they eat earlier from your house to get to school?
If you do email, try to do it in a one/two sentences, direct to the point. Like a business. If he gets along with ex, then keep up the communication back and forth with just one answer.
In court, most of those type of issues are considered different parenting styles. As long as they have food, bed, clothes, she really can not do much. The kids are getting older so you can start talking to them more about issues that have to do directly with them and see where this is coming from. If he does it without you, then may tell him more and not want to hurt your feelings about certain things.