In G.Martin's books and series, who was the first married man about whom we know that he joined the Night Watch (by his own will, or being sentenced to do that) while his wife was alive?
The first in terms of living people for the series was Mormont, who joined the knights watch after he had already had legitimate male son to take over from him as Lord of Bear Island.
The first is lost to history, although it would have almost certainly been a founding member of the knights watch after the "long night" after which the Knights watch was founded.
There are only two examples that I can find but no explicit mention is made about a wife so we can't really know for sure.
Jeor took the Black so his son, Jorah, could inherit Bear Island and become Lord Mormont. However, no mention is made to his wife and whether she was alive at that time.
"It is," the Old Bear told him. "It was my father's sword, and his father's before him. The Mormonts have carried it for five centuries. I wielded it in my day and passed it on to my son when I took the black."
A Game of Thrones, Jon VIII
Again no mention is made to a wife but he does have true-born sons; the eldest of which is to become Lord Slynt. If he has true-born sons he must have had a wife at some point but it does not mention if she was alive at this time.
"Dwarf?" His anger flashed. "You should have stopped at Imp. I am Tyrion of House Lannister, and someday, if you have the sense the gods gave a sea slug, you will drop to your knees in thanks that it was me you had to deal with, and not my lord father. Now, how many sons do you have?"
Tyrion could see the sudden fear in Janos Slynt's eyes. "Th-three, m'lord. And a daughter. Please, m'lord—"
"You need not beg." He slid off his chair. "You have my word, no harm will come to them. The younger boys will be fostered out as squires. If they serve well and loyally, they may be knights in time. Let it never be said that House Lannister does not reward those who serve it. Your eldest son will inherit the title Lord Slynt, and this appalling sigil of yours." He kicked at the little golden spear and sent it skittering across the floor. "Lands will be found for him, and he can build a seat for himself. It will not be Harrenhal, but it will be sufficient. It will be up to him to make a marriage for the girl."
A Clash of Kings, Tyrion II