Offer an alternative way to fulfil the quest
It‘s unsurprising that the characters try to get her to come back, as the quest is described thusly (p. 10):
The local midwife — an acolyte of Chauntea named Adabra Gwynn — lives by herself in a stone windmill on the side of a hill a few miles south of Phandalin. With dragon sightings becoming more common, it’s not safe for her to be alone. Urge Adabra to return to Phandalin. Once she’s safe, visit Townmaster Harbin Wester to claim a reward of 25 gp.
It is easy to mistake the quest as "get her to come back to Phandalin", and the characters have reason believe she is not safe by staying alone, after all they just saved her from a perilous situation if the quest plays as described. The quest however offers this solution (p. 46):
Adabra declines to return to Phandalin, but the characters can complete the Umbrage Hill Quest (...) by asking her for a note for Harbin Wester confirming her safety.
If the characters cannot think of asking themselves, you can have Adabra suggest she writes the note for them, to confirm she now is safe and satisfy the quest giver, Harbin Wester.
As an added note, while her abode protected her this time around in the encounter, my read is that she is indeed not safe and is misjudging her situation. If the monster was bought off and returns with its mate, or if indeed the dragon would pay her a visit while the PCs are not around, she might well be in peril. So it makes sense for the PCs to think it will be safer for her to return with them.
An alternative solution is that you allow the characters to persuade her to change her mind and follow them back – for example, through roleplay, or a successful if hard Charisma (Persuasion) check.