Robert gets to them and attacks Olivia. He tricks a local woman into giving away their whereabouts.
She has sent the children to hide in an old bomb shelter bunker, which is the room in the drawing from earlier in the story, but they come back to the house because they are scared. He has tied Olivia up and is threatening to rape her but instead when the children return he grabs them and disappears.
The police find her and a search for the children starts.
They find Robert with them at the top of a cliff and he's trying to hang onto them all and jump. They break free and are safe.
I have forgotten what happens to Robert at that point, but Olivia and the children are safe.
It was all just a bit predictable really, so you've probably already guessed all this.
One thing that I think was a flaw in the plot was that Olivia and the children had been to Alderney three times already before they moved there, so they seemed more local and not like newcomers when they finally made their escape. But Olivia had to change their names and dye their hair when they escaped, so they looked different anyway. She wouldn't have been able to do that for a week's holiday and not have Robert notice the change in hair colour, so I felt that was a wobbly bit of the plot.
The twist at the end was that Robert had killed Olivia's previous boyfriend (Dan) and buried him on Saddleworth Moor.
Robert had stalked her through college without her noticing and was the person chasing her at the start of the book. Dan was the man whose arms she ran into and Robert killed him and her parents.
Olivia has worked this out because he took her to the burial site and made a comment that she could be standing over a body right at that moment and never know it.
So she confided in Dan's brother, but instead of going to the police and having them dig for a body they decided to take blood from Dan's brother, spread it around Olivia and Robert's house, have people claim to have seen Dan visit and set him up for the fake murder of Dan several years after he really did murder him.
For that to work Olivia had to claim to the police that she slept with Dan's brother and he was Jasmine's real father. Because they took DNA from Jasmine to match it to the blood in the house and knew it would show up as being from her uncle rather than her father. So they had to pretend her uncle was her father and her father was her uncle.