Was colonial America more affected by transatlantic trends or local influences in the areas of politics, ideas, and social life?
To me, it is clear that colonial America (at least the parts that are now the United States) was clearly affected more by transatlantic trends than by local influences.
You can see this in social life from the fact that most of the luxury goods that the colonists used came from Europe. Many of the richer Americans sent their children to be educated in England as well.
In the area of ideas and politics, all you have to do is look at the Declaration of Independence. It is based on the ideas of Enlightenment (a European innovation) thinkers such as Locke and Montesquieu.
I would also agree that early colonial culture was greatly influenced by the mother country. Fashions, art and literature of the 1700's all contain obvious European influences. Schooling was modeled after the English and much of the literature read was produced by European writers and philosophers. Wealthy colonists held onto European trends longer because it was the fashionable thing to do. However, there are signs that the colonists were developing their own unique culture as society became more established. American painters portrayed the features of their new home such as the distinctly American fauna, flora, landscapes and people. Cuisine evolved around what could be grown in America influenced by Native American and African styles of cooking. As generations passed Americans developed their own styles of music, teaching, dance and dialect. These styles may be a hodpodge of European, African and Native traditions but it is a style none the less.