This is a very good question. In general, it's a good idea in matters of discipline and values to present a united front.
No, you can't watch television now. Mom said no. No means no.
I agree with Daddy. It's better to be honest than to be right. Let's talk about why.
However, whenever two people come together for any length of time, conflict is bound to follow. We also owe it to our kids to show them how to disagree respectfully and set healthy boundaries for ourselves. Matters of truth should take precedence over agreement. Matters of respect should as well. For the first,
No, Honey, I think (child) is right about that. Maybe you're thinking about (Y)? (X) was where (Z) occurred. We can look it up if you like.
The second is trickier. A personal example might be better.
My ex was very parsimonious even though we had plenty of money. At one point, he was doing all the cooking and shopping. (He was working half-time; I was working half-time, homeschooling full time, and the kids and I were doing all the other chores, including farm chores.)
Because shark meat was cheap, he would buy it all the time. The kids and I didn't like shark, and we told him that (politely) many times. But it was cheap, so he continued to buy it and serve it.
I taught my kids not to complain in general about services done for us, and to be gracious.
One evening, he called us to the table. "What's for supper?" asked one of the kids. "Shark," my ex answered. We were all silent. Finally I said, "I'm sorry, but I'm not eating it. You know we don't like shark." The table erupted. "If Mommy isn't eating it, neither am I!" the kids cried. This was treason!
The thing is, we had all told him many times how much we disliked shark, both in private and together. We didn't need to eat cheaply so often. He was putting his own desire to save money (for what? We had much more than enough money) before our desires. By speaking up and drawing a boundary, I was saying, "We are important, too. You need to respect our feelings, too. And you're not doing that when you buy shark." We had toast and scrambled eggs. He had shark.
He never bought shark again, without another negative word ever being said.
Respectfully disagreeing and healthy boundaries need to be taught and modeled for kids, or they will have a very erroneous belief of what marriage and life with other people really is.
I wouldn't want my kids to feel like their marriages were defective because they didn't agree on everything. Or that every authority figure was always correct.
Having said all that, I'll add, pick your battles wisely.
I want to add that we had weekly family meetings where anything could be discussed. This was helpful to us.