We are a family of four from Denmark flying in to California mid July. We will rent a car in LA and travel to Seattle over 3-4 weeks. From Seattle we will mid-August leave USA via train for Vancouver, Canada. We will stay in Vancouver from mid August to January 2016, having a return flight ticket Vancouver-Copenhagen.
If we buy train tickets Seattle-Vancouver before entering USA, will this be sufficient to obtain ESTA?
Yes. You just need to show your intention to depart. A train ticket (plus your ticket from Vancouver to Copenhagen) is certainly enough.
In the past, I've bought Greyhound bus tickets from Seattle to Vancouver - they did actually check them and were fine with them as well. One of the times I did this I was flying into Boston first, and even though it was a bus ticket on the other side of the country, it was fine.