I think you have confused being a good father with being the father you wished you had had. Being that you didn’t have stable and nurturing parents, you never learned how to temper love with discipline. In your experience, a parent shows their love for a child by giving him or her things, you even believe that money is the foundation of your marriage, but money and gifts can’t buy genuine love and respect.
Your wife is a by-product of a loving but disciplined home and she is raising your children in the same manner – this is a good thing. Then you come and try to be “super-dad,” over-riding her words and disrespecting her in the eyes of your children – that is not a good thing! When you devalue your wife and validate your children’s disrespectful behavior toward her, she cannot be faulted by wanting to walk away.
Parents must show a united front. Disciplinary measures should be discussed in private between the two of you and presented to the child by both of you. This way the child knows that he or she cannot play one against the other. Children learn by example and the example you are showing them is one of divisiveness, disunity and disrespect. These are the lessons they will carry into their own marriages. Is that what you want?
In terms of your wife: Begin by reaching out to her and trying to explain what your childhood was like and why you react to your children the way you do.
Tell her that you see how hard she works to teach the children values and good character traits, and that you admire and respect her. Discuss the logic in disciplining the kids together and how to come to decisions you are both comfortable with.
Speak with your children and make them aware that from this day forward decisions will be made by both of their parents.
And, most importantly, do not hesitate to reach out for professional help along the way.