Any thoughts on how petunia reacted after they find harry on the doorstep?
This is probably a little more than you were asking for but….
Once the shock died down I think Petunia’s major feelings were probably guilt and maybe even some regret, which is what led her to take Harry in. We saw in The Prince’s Tale that Lily and Petunia were close as children, but we could also see Petunia always feared the magic Lily possessed…but she was also jealous of it, as we saw when Lily and Severus found those letters between Petunia and Dumbledore with her pleading to let her go to Hogwarts too. So after she found she couldn’t go, she began to resent Lily and I think a small part of her was hurt that Lily chose to go off to school and leave her behind. And then having Muggle parents, naturally they were enthralled by the tales Lily had to tell about her time at school, which would make Petunia feel left out and her resentment continued to grow (”But for my mother and father, oh no, it was Lily this and Lily that, they were proud of having a witch in the family!“). It grew so much that she began to hate magic and everything and everyone associated with it, leading her to strive for normalcy. She found it in Vernon Dursley, who was a normal man, with a normal job, and they lived in a normal house in a normal neighborhood and had a normal son.
But still, Lily was her sister, and it did seem like she tried to keep some kind of relationship with her even after she went off to Hogwarts…but it seemed to always go wrong. Lily mentions in her letter to Sirius that young Harry smashed a horrible vase Petunia had sent her for Christmas which, although Lily found it ugly, was a bit more thoughtful than the old socks, single tissue, etc. Harry got. Also, we know there was that dinner that went horribly between James, Lily, Vernon and Petunia, and then Petunia refused to let Lily be a bridesmaid at her wedding and Vernon refused to talk to James at the reception, calling him “some kind of amateur magician” within earshot, which was probably the last straw for both parties, and was probably the last time they saw each other face-to-face. The last correspondence between the Lily and Petunia was that Harry had been born, which Petunia threw away immediately.
And suddenly one day Petunia goes to put out the milk bottles and finds a baby on her doorstep. A baby, who was most likely startled awake by her scream, blinking up at her with a nasty cut on its forehead and her sisters bright, green eyes. She probably snatched Harry up and brought him inside, not wanting the neighbors, no doubt peering out their windows to discover the source of the scream, to see a baby sitting on their doorstep. Vernon would have come hurtling down the stairs asking what was wrong, and started stammering at the baby in her arms. She would have plucked up the letter in Harry’s blankets and read it very quickly. And then she read it again, more slowly. And one more time to ensure the words on the page were real.
Did she want Harry? No. Did she love him like her own son? Obviously not. But she took him. Lily had died for her son, and if Petunia did not take him in, it may have been for nothing. Harry would still be in danger, but she understood that by allowing Harry a place under her roof, it would seal the blood magic Lily’s death had left on him and keep him safe, at least for now. Petunia had already lost her sister over a year before, but now her sister was truly gone. Not just dead, but hunted down and murdered. Petunia never knew the danger Lily was in, and she probably felt guilty for that. Her sister had been targeted, forced into hiding, and murdered in her own home, and Petunia hadn’t the faintest idea until then. Petunia may have resented Lily but surely she never wanted her dead. But she was gone. And so were Lily and Petunia’s parents. She was the only one who could help Harry, and begrudgingly she took him. Harry, who would be a constant reminder of her sister and the world she could never be a part of, knowing one day he too would get go off to the school she never could. But she took him.