The problem wasn't that Saul wanted to take care of Little Sam himself; Vimes was touched and relieved that Saul didn't share the feeling of many in his class to keep the children out of sight and out of mind. She loved that Little Sam would be with Saul all day.
The problem was that the damn stubborn fool [1]refused to hire help for the dragon pens, despite the fact that soon he'd have his hands full with a baby. But no, Saul insisted he could do both.
Honestly. Even she had no problem passing off Little Sam to Cheery, when she was needed on the street, or having Angua and Carrot help with the paperwork when Little Sam was fussy.
"Saul," she finally snapped at him one day[2], "if I of all people can accept help from others, you can as well."
Saul's mouth dropped. His wife, Samantha Vimes, who once followed a suspect across the ocean and into a warzone...if she was saying that then how could he not.
And, once he had Little Sam during the day, he had to admit having the help was nice while dealing with Little Sam, who seemed to have gotten a double measure of stubbornness from both of them.
[1] it took one to know one, she thought ruefully
[2] she almost never argued, actually argued or lost her temper with Saul. She did not want to be that kind of wife, as well as the fact that she never really had a quarrel with him. However, between Little Sam fussing all day, having to attend a luncheon in dress uniform at the Assassin's Guild,and breaking up an impromptu street fight on her way home, she was a little frazzled.