If she gets gifts or not.  She most likely has mental problems.  Either way she is going to feel picked on. She only got one cell phone. Not a cell phone, tablet, gaming system ect. 
Let DH do what he wants to ease his guilt.  Let him feel that he tryed.  Do not interfere with the gifts because it's going to be all your fault in the end.  He can not blame himself, he will not blame BM,  so who is left. You.

Do not used any of your money for her gifts. 

I would lean toward agreeing with BM. I'm guessing dad either doesnt want to be the bad guy or he doesnt want to miss out on having a fun Christmas so hes putting that before actual parenting.

I'm also a teacher, and parents need to set the example.

If they fail out of school, or cause problems daily, then they need to be shown that there is no incentive for that kind of behavior.

No education and bad behavior, when these chilren are adults, is going to lead to a bad person. Any parent who condones behaviorj like that is setting up another welfare king/queen, and they are always a leading factor in why many schools have less certified teachers than non-certified teachers.

DH plans to give SS10 the gifts purchased for him (specifically a Nintendo Switch Lite and gems) and then taking them away.  SS10 is having problems "remembering" to turn in work, behaving in class, etc.  He is currently restricted from electronics until he gets two weeks of neutral or better behavior reports from his teachers.  

SD about to turn 15 has an F in math and many missing assignments.  She is on Wifi restriction until that gets better.  She will get gifts, but literally nothing she's getting will excite her at all.  

Their BM does not believe in holding kids accountable, soooo...  DH does all that heavy lifting.  He feels like a prison guard a good portion of the time, especially with SS, where the issue is behavioral.  Juststressed is right, if a parent doesn't set an example and teach kids about respect and accountability, they will not learn it and then he's failed as a parent.  DH does not want to fail.

I don't personally think kids should lose birthdays or Christmas for bad behavior.  Set limits and discipline in some other way.  

take away birthdays or Christmas for behavior issues. That was always my hard line. Holidays are untouchable. 

Are there some natural consequences that would make more sense for the behavior? Or even daily privileges that can be removed? Unless the act is directly related to Christmas then taking away Christmas has nothing to do with the behavior. I am also a big fan of "community service" "school service" and "family service." When my kids were younger and if there was a behavior issue, I worked with their teachers to come up with something they could give back to the school. Washing desks, helping a classmate, etc. Then at home they had something they could do for me since my time was spent dealing with their behavior. Community service was to teach them to be thankful and also get them involved in the community. 

Withholding Christmas Gifts is very sad and not effective.

 Similarly taking 'away' electronics for a day, two or three is also not effective. EARNING TV time or gaming time for good behavior does work.  Find the Childs currency...find the currency.

Ill advised to follow thru with no presents at Christmas.

YOU don't have to get her anything for Christmas, if you don't want to, but her parents need to figure out something else to get this kid under control.

I agree with not using Christmas as punishment. But those gifts would be the first taken away for bad behavior or grades afterward.