That wasn't what it was about in the book. There is no mention of his christening because she most assuredly did it. Uhtred was away as a hostage when the child was born. Alfred had used Uhtred's rank as an ealdorman by birth to make him a hostage and used subterfuge to draw Uhtred to him and then it was sprung on him that he was summoned only to be given as a hostage. Uhtred has a lot of cause to hate Alfred early on and this is part of it. His name as Uhtred, Ealdorman of Bebbanburg was what was passed and accepted by Guthrum as hostage. In the books, Mildrith is a reeve's daughter, below an ealdorman in rank as reeves are thegns.
Once he is saved from death by Ragnar the Younger, who stops Guthrum from killing Uhtred along all the other hostages, he is understandably outraged with Alfred and goes back and tells Mildrith that they are going to live among the Danes. That's what gets her back up. It's only because Ragnar himself becomes a hostage that this does not happen.
Furthermore, Alfred knows that it was Uhtred who killed Ubba and won victory of Cynuit, too many men saw him do it, and he also knows that Uhtred did not participate in the attack against the monastery at Cynuit, that was Svein's work, but still grants trial by combat to him and Odda the Younger's champion, Steapa in the books rather than Leofric, a fact that only comes out later on. It's true that Uhtred settled the debt on Mildrith's land with plunder stolen from other Christians, but as he points out, he did not directly steal it from them, he stole it from other Danes, being Svein of the White Horse.
So early on he does have just cause to be very angry with Alfred.
Alfred also sent him to Leofric to try to humble him, and tells Beocca that Uhtred must be broken like a horse. But Uhtred tells the priest he is not a horse but the lord of Bebbanburg and then laughs and says Alfred wants him to become a meek Christian. Beocca asks if this is such a bad thing. Uhtred telsl him it is, because when the Danes come Alfred will need proper men to fight them. At the same time, Alfred's sheltering him saves him from Kjarten, the man who killed Ragnar the Elder. So early on, there is mutual saving of each other. They both do, numerous times.
There's a lot of backstory, too, because when Uhtred was a child Alfred had tried to make him into a priest. But as Uhtred points out, the Danes made him a warrior, and Alfred needs him more in that respect.