Once Jenkins had murdered Billie Jo & calmed down, he had to go straight out into the car where his children were waiting.
He couldn't try to save her once he realised what he had done. That would mean telling the children to come back into the house & implicating himself.
He can't try to save her without telling the children, sooner or later they will come back into the house of their own accord & see Jenkins with a battered Billie Jo. Which again implicates Jenkins.
It's doubtful he considered trying to save her. Her injuries were too bad & an alive Billie Jo would implcate Jenkins.
So Jenkins went straight to the car & drove the wrong way to a DIY store with no money or cards. To buy White Spirits which wasn't needed as there was already White Spirits in the house.