I have read "The Rose Tattoo" but never seen it. No critic ranks it with the best Tennessee Williams. It is generally considered a comedy although many reviewers of the first NYC production found a confusion between the play's sentiment and slapstick.
Williams dedicated the play to his first and probably only real love, Frank Merlo, described as both rambunctious and decent. My favorite anecdote about Merlo is that Jack Warner, the owner of the eponymous film studio, was somewhere--exactly where changes with who is telling the story--and turned to Merlo and asked pugnaciously, "What do you do?" Merlo immediately responded "I sleep with Mr. Williams." This happened in 1949 perhaps. At any rate, LONG before Stonewall.