Because of FERPA, I can't share what I've seen in 15+ years of working in special education.
But I can make up some scenarios as to how a parent gets called to take a child home over and over again: (using my knowledge of how classrooms/programs are set up, how public schools work, no actual info about any student I've known/worked with)
Student A is a nonverbal child diagnosed with autism, with a selective diet, sleeping issues, and a tendency to strike out when hungry or tired. Parent has been up all night with child, who has not been sleeping well or eating well because of having a cold. (Kids come to school when they have a mild cold) Parent drops child off at school, (sharing info about hard night), goes to work.
Student A is tired, cranky, wants snack now, doesn't follow directions, misses out on something he really likes because he's busy trying to get his snack, and then has a meltdown when he realizes he's missed his favorite morning something-or-other. Classroom has many other students (inclusion is the rule) so they can't repeat the morning thing because that messes with everything else that has to be done.
Paras try to redirect, teacher has to take other students out of the room because of meltdown (now that routine is messed) student A gets needs met, calms, class continues, but the cycle starts over and over again. Student A is taken to different location, that sets off another meltdown (because he's so tired, the poor thing, and needs sleep but can't at school - letting a kid sleep all day means he won't sleep that night!) and it gets to the point that he needs to go home. They can't meet his needs at school. Mom can choose to let him sleep, but the school can't.
This happens every few days because the kid's sleep cycle is screwed up, he's got a mild cold (no fever) or a lasting runny nose/cough that just keeps him up. Then it clears up, things get settled, and something else messes up the cycle - like the store doesn't have the right chicken nuggets, or the school lunch was changed but not put on the schedule.
A child who acts out when distressed is hard to deal with at school. There are many, many rules and regulations and policies that have to be followed, for the safety of all the children and the staff. Sometimes sending the child home is the last step before calling law enforcement/ambulance.
From the bit of info that the child gets sent home a lot, and doctors don't want to deal with him, it does sound like he has issues that mom is either denying, ignoring, or refusing to take care of. A child with issues that send him home from school/get him removed are most often safety issues. I hope the mom is safe as well.