First, Nico saved Laura from drowning and both went back in time - though we don't yet know how or even completely why. Laura's reason is to save her daughter. Nico's is to save his brother from the death of death row. The two are connected in that the governor's decision to carry out Nico's brother's punishment was ultimately triggered by the horror of Laura's daughter's death - but we don't yet know the deeper connections of these two stories, which there no doubt are.
The prime ground rule is one we've come across in many a time-travel story, including my own. The past is tough to change. History is recalcitrant, is the way I like to put it - the universe puts up whatever obstacles it can on behalf of the original history, if we can call it that (but, who knows, perhaps that itself is a changed history, a sequence of events brought about by some time traveler). So Laura's daughter gets an allergic attack on the plane, which obliges her to go back home to California (where she'll be killed in the original timeline) rather than safety in Hawaii. And some neighbor helpful to the universe brings back the red shoes which Laura was trying to throw out - so they wouldn't be discovered along with her little daughter's body.
Nico and Laura also do their best to the stop the serial killer in one of his earlier killings, in one of the best sequences of the episode. They come close, but fate and the universe prevail.
All of this means that we'll be in for some good times in this limited series, and I'll be back after the universe shows it has in store for us after the next episode of Somewhere Between next week.
See also: Somewhere Between: Frequency meets Awake