"We’ll stay for three days and then go home. I’ll wire right away for steamer tickets."

Steamer Tickets

RMS Scythia which sailed from New York to the Mediterranean in the mid 1920s.
Public DomainRMS Scythia which sailed from New York to the Mediterranean in the mid 1920s.

A steamer is, quite simply, a ship or boat powered by steam. In this context Rosemary’s mother is referring to the ocean going liners, of which the ill fated Titanic was one, that were the primary method of trans-Atlantic transport in the early 20th century. The popularity of air travel in the second half of the 20th century lead to the decline in the use of ocean liners and the RMS Queen Mary 2 is the only one remaining in active service today.