Depends on the court. Here, they don't understand. My mom was my son's only caregiver when he was a baby and I was working. We live in the country, no other family close by. My mom didn't have a working car at the time, and depended on me for transportation.
She got summoned for duty, and called to see if she could get out of it as the only sitter we had while we both worked. They told her absolutely not. She would have to have us take off work and she would have to find transportation (it is about 20 miles from here to the courthouse) and that was that.
Luckily she never got the final call, only the preliminary notice, so we avoided the issue, and now is old enough to be excused.
I'd suggest getting right on the ball with securing a doctor's note about your mom's condition, and needing care. It may be enough were you live, but might not be. Best wishes and I hope you are able to be excused.