Could the older woman have been Glynis Johns? There's an oldie called "Zelly and Me" (1988) in which an older woman (the grandmother) takes care of a young girl and, essentially, ignores her. I don't remember if she burns herself.
EDIT: I'm almost positive this is, indeed, the movie you are looking for. I refreshed my memory by finding this review:
"A strict grandmother who's only duty is to prevent her grandaughter from being rebellious like the girl's mother, never seems to provide enough love for her. When Zelly notices Phoebe BURNT HERSELF, CoCo fires Zelly, and pushes Phoebe into her parents bedroom because "she's now a big girl" and throws Phoebe's toys including her Teddy bear away. Zelly tries to rescue Phoebe, but at the last minute she and her boyfriend who attempted to kidnap her knows it's wrong, and sends her back. Phoebe, must face the fact of living with her strict Grandmother, and with a pair of white socks makes a doll for herself."