I can see how frustrating you feel in this situation. Both of you love your kids. Both want them to have a great childhood and a happy home. However, every relationship needs rules.
You could have a talk with your wife and ask her why she feels children should not be disciplined? Be honest and be willing to listen. Does she feel your methods are too strong? Discuss what behavior can be accepted and what cannot. Convey to her why you feel there has to be rules, otherwise, children will have issues later in life. It does not mean you do not love your kids. You want them to grow up with appropriate values.
Together arrive at not acceptable misbehaviors, and their consequences. That is the penalty the children have to pay for the misbehavior. Some time out, some household chores, etc. What ever you and your wife together feel is appropriate.
Then both of you will have to impose that penalty. Explain to the children what consequences will occur when they misbehave. Let them know in advance. And when they misbehave (they will to test you!), then impose the penalty. Both you and your wife will have to be on the same page.
All children will play one parent against another. So you both will have to be alert.
Also it will help if you and your wife do spend some time alone, like a date. At regular intervals. Focus on each other, talk about goals, future, dreams, etc. Connect as a couple; then parenting will come naturally.