...and without a family to manage, he is disqualified.
No, the qualification is "able to manage." The family is a place where such would be evident, but not the only place.
How are both stated? It only states that he is to manage his family well...kids or not. It does not state "must be the husband of one wife...must have children".
What do you mean "How is it stated?" It is stated in words. It says "keeping his children under control." Children is plural, which means in your system of interpretation he must have more than one. And if he doesn't have them, how can he keep them under control?
If he was the husband of one wife at appointment...so?
Notice the text does not have "must have been the husband of one wife at some time.' It says "must be..." That is present tense. If you don't have a wife, you can't be the husband of one wife. And if your wife died, you no longer have a wife.
..maybe to you it is, but in the context of the chapter it is not.
You live in a strange world if you think a wife and children are te same thing. I have a wife and a child, and I can tell you for sure they are different. The issue with the wife is sexual integrity; the issue with the children is management ability. These are two prominent areas where those qualifications would show up.