This isn't a "mean boss" this is a practical boss. She is calling you on the carpet for job performance, which she is allowed to do. It is NOT your place to say if she should be in management. If you think you can do the job better - tell the Director or President and give solid reasons why you think you would be better at the job than she is. Then you can figure out the other side of the coin....
I don't know what you do for a living or what your job entails. I do know that when I worked at Kindercare, to have my employees call in sick could upset the whole center...especially if they made a habit of it....it was lack of responsibility to have back up care in place (yeah, I know it's a day care!! go figure!) and performance...
She is the boss. Is she following the company rules on time management? If so - then you are upset that she is calling you on the carpet. When one person is out - it CAN affect the whole department. So it's NOT JUST ABOUT YOU. You are part of a team, right? The TEAM DEPENDS UPON YOU to be there to do your part.
I understand that you are a mom. However, you are a working mom and now you need to have back up care for your kids when they get sick. Maybe share the duties with your husband?
Three days when a family is sick? That sounds excessive to me. Personally. If you already know that one gets sick - be proactive and get the clorox out and wipe down all the surfaces - door knobs, walls, banisters, faucets, etc. to keep the virus or bug from getting to others...have your other children wash their hands more frequently. That's being proactive.
Double standards? Document them then. Don't just complain about it. If you have proof of double standards, prove it.
You have migraines? Get a note from your doctor when you suffer from one so that you have proof of sickness.
Yes. She can take it to HR. If you can't perform your duties because you are calling in sick, then yeah, you can get in trouble. Document. Show proof.
It is my opinion that you are upset for being called on the carpet..don't play the victim. Be proactive. Prove that you are capable of doing your job and the team won't suffer. Don't like her as a manager - document things and if you think you can do it better - go for it.