Are the marshall islands part of polynesia?

No not any more.

They were a U.S. Territory from 1947 when the U.N. gave the islands to the United States for a strategic trust. In 1951 the U.S. Department of the Interior took over the island's administration. From 1946 until 1954 the islands and water's just off the islands were used for Nuclear test's.

In 1986, independence was attained under a Compact of Free Association with the United States.