When I was in kindergarten we watched a slightly disturbing movie about an introvert witch and two twin girls about 11. I can't remember much except that the mom constantly told the girls that the witch didn't like company, but they didn't listen and went to the witch's house, but for some reason the parents came with them but were very nervous. And at one part, the girls made a promise to the witch that involved the phrase, "Cross my heart and hope to die, stick a needle in my eye." If it helps, I remember the witch always wore black, and I remember one scene where the two girls were skipping across a bridge but stopped to look at the witch's house.
Sounds like you're thinking of Double, Double, Toil and Trouble.
This is a screen shot of a quote taken from IMDB - does it match your "Cross my heart and hope to die, stick a needle in my eye"
Outside of that quote, it features twin girls (Mary-Kate and Ashley Olsen), albeit younger than your description (they would have been about 6-7 years old at the time of filming). The witches involved are their Great Aunts Agatha and Sophia, another set of twins. The parents approach Aunt Agatha for a loan, which might account for their nervousness. Sophia has not been seen in years, which could be interpreted as that she was a shut-in, similar to your commentary about being introverted.