My oldest daughter had a similar problem. Hearing is good, but singing is false! My wife and I both have a musical education, therefore, at first we studied with her at home:
They tried to sing along with her or play a melody on the synthesizer so that she could "tune" to us or the instrument.
They tried to record her voice and let her listen.
They suggested she sing into a microphone (so that she could hear herself online).
They showed how to sing "with the hand." This technique: you hold your hand at chest level on weight, as if sitting at the table. If the melody goes up sequentially, you raise your hand up sequentially, as if by steps. This technique is used to understand pitch changes).
They tried to sing, covering one ear with a finger (this technique is used in vocals to hear the sounds made by the inner ear).
Positive dynamics, of course, was, but still, it didn’t always “hit the mark”.
After all our efforts, we decided to practice singing with our daughter professionally - and we hired a vocal tutor - a vocal teacher from a music school. She immediately told us "practice, practice, and nothing but practice is needed if there is a rumor!"
She asked the same exercises (described above) to our daughter plus exercises for diction. Classes with the teacher were held in the regime: 2 times a week, for an hour, throughout the year.
These systematic classes helped my daughter learn to control her voice and a year later she was accepted into the choir!