I would put it in a sports analogy to hopefully help your kids to understand. Families are different just like teams are different. The difference doesn't mean one team is superior or less functional than the other, it just means they have a different way of obtaining the same results. Both your family and your wife's family love each other very much but have different ways of expressing mutual affection toward one another.
For example, me and my kids rarely sit down at the dinner table and eat together. Most families would frown on this, however, it's worked for me and my two kids. We get along GREAT! We never argue and the three of us are very close. My daughter is 16 and my son is 17; I've raised them as a single parent since they were 3 & 4 yrs of age.
There is no way to force love or camaraderie in a family, it has to come natural. When a family, especially involving kids, is forced into doing something, or it's contrived in any way, the kids will do it, because an adult said so, but the repercussions of that can be negative.