tenses - Please help me understand when to use -ing on a verb

There are two questions I'm struggling with.

(1) That I have little interest in art is not the fault of my parents,
taking me to art exhibits and galleries from the time I was ten years old.

Why is the "taking" wrong? I'm guessing it has to be "who have taken" because of "from the time I was ten years old" but I still don't understand why it's wrong to say "taking." The word "parents" comes right before the comma so it shouldn't be an ambiguous modifier. After all, wouldn't it be correct to say the following:

Taking me to art exhibits and galleries from the time I was ten years
old, my parents are not at fault for my having little interest in art.

My next question:

(2A) Though she missed her old friend, Sharon was generally happy at
her new school, having much smaller classes than her previous
school.

(2B) Though she missed her old friend, Sharon was generally happy at
her new school: it had much smaller classes than her previous
school.

I know why (2B) is correct, but I don't understand why (2A) is incorrect. The modifier "having much smaller classes than her previous school" is correctly describing "her new school" so what exactly is the problem?

Thanks in advance!