It's Terra Nova. Valorum gave the answer.
The series is initially set in 2149, when overpopulation and declining air quality threaten all life on Earth. When scientists discover a temporal rift permitting (one-way) human transmission, they initiate a series of "pilgrimages" to a parallel "time stream" resembling Earth's Cretaceous Period. The series focuses primarily on police officer James "Jim" Shannon, his wife Elisabeth, and their three children Josh, Maddy, and Zoe, as they join the colony there, named "Terra Nova" (Latin for "New Earth" or "New World").
Elisabeth Shannon is chosen to join Terra Nova for her medical expertise, and her two older children with her. Her husband, imprisoned for violating population control by harbouring a third child and assaulting an official agent to protect his young daughter, stows away to join them and eventually convinces the colony's leader, Commander Nathaniel Taylor, that his own police expertise is of use to the administration.
Opposing the colony and its leader Taylor is a group of separatists known as the "Sixers", so called because they arrived in the "Sixth Pilgrimage", working in concert with corporate industrialists to strip the Cretaceous Earth of its resources and transmit them to 2149, allowing for massive profits at the cost of environmental destruction. It is later revealed that Commander Taylor's estranged grown son, Lucas, is working with the Sixers as well. Toward the end of the series, Lucas perfects travel to and from the future, thus enabling the industrialists, with a private army called "The Phoenix Group", to invade Terra Nova. At the end of the series, Jim Shannon returns to 2149 to destroy the gateway permitting travel to the Cretaceous, whereupon the Phoenix Group retreats to the nearby "Badlands", leaving behind a wooden ship's figurehead apparently located there by another temporal rift.