It was a good idea for the magical woman to give Mother a fairy daughter, rather than a human one. With fairy's growing up so fast, Mother was able to raise Thumbelina, watch her get married, and presumably give her tiny grandchildren. Had Thumbelina been a human living a normal life span, Mother would probably have died of old age before her child was fully grown.
That might have less to do with her being a fairy and more to do with her being born from a flower...
Continuing that idea; tiny semi-adult? Inconvient, but still easy to take care of. Tiny baby? Accident waiting to happen.
The fairy brings the old woman a flower bulb that contains Thumbelina. The fairies apparently come from flowers as well. Thumbelina gains wings at the end of the story just like the other faries. That means that Thumbelina could've been a fairy all along, and the fairy woman knowingly kidnapped her from her people.
It wasn't a Fairy the old woman went to, it was a good witch. She just looked like a fairy, but it was probably a glamour spell, as witches are known to do.
Mrs. Toad's actions become a good bit more disturbing when you know more about the fine tradition of bridal kidnapping.
The plot in general is a lot more disturbing when you consider that it consists almost entirely of a naive girl being kidnapped from her home and being used and tricked by nearly everyone she meets (even the bird is too obsessed with being a Shipper on Deck to get her safely home). And a lot of those people want to marry her, even though they're different species.