I think Mrs Dashwood shared her husband's faith in John's promise as she did not doubt the sincerity of his assurance.
To me, this impies Jon and Mrs Dashwood had a favourable relationship, outwardly.
However, I doubt they were much able to develop a mother/son bond.
Mrs Dashwood appears a warm hearted lady who wanted to believe in John. Yet I wonder if her step-son was responsive to her willingness to be a mother or friend to him.

If John went away to school at an early age, he may have felt distant from his father and insecure. Later, his step-mother would be busy raising children and he probaby saw his father's fondness for them.
'Mr John Dashwood had not the strong feelings of the rest of the family'. (ch.1)

John was more vulnerable to Fanny's influence than the Dashwoods realized. By his wife's apparent deference and persuasion, John resolved to provide no financial assistance to his father's widow.
Fanny's final point in regard to his promise to his father is of interest;
'Your father thought only of them...he would have left almost everything in the world to them.'
She pressed the right trigger- John was reminded of who was so dear to his father, and his step-mother was cheated out of promised money and protection.