Doc adamantly does not want Mel to help him at his practice. He tries repeatedly to push her away but she doesn't budge. She continues to prove her worth to him and he soon warms up to him. She helps him with his patients, showing how seamlessly they can work together. Together they save a whole family from being poisoned, rushing them to the hospital.
It's then that Doc realises how important Mel has become to his practice and to Virgin River. At the hospital while they're waiting to hear about the family they've rushed in, he offers to bring her coffee, which she can see as a peace offering. He asks her to stay on at the practice, even adding her name to the sign outside the door and making her coffee when she shows up for work.
Doc also seems to maybe want to make things work with Hope if that last kiss is anything to go by.