First, the trauma designation of a hospital doesn't have anything to do with your experience in critical care, unless you are working specifically in a trauma ICU. I would look more closely at whether or not it's a teaching hospital or private. Your work (& learning) experience will vary depending on whether you're collaborating with residents or attendings.
It seems odd for a large hospital to have an internship program that doesn't lead to employment. Have they told you this? I understand that it shouldn't be guaranteed, but it seems like it should be the goal, if the match is right. Have you asked how many of the last group of interns are working in an ICU? Check it out a little more in-depth, if you have questions to clarify.
If getting a position is difficult, I would agree with smiley and go for the SICU. You can always look elsewhere later on (though many hospitals want 1-2 yrs to consider you "experienced"). You'll be much more marketable and competitive when you have experience.
In the end, you're looking for the same thing anesthesia schools
are looking for: titration of multiple vasoactive drips, vent management, invasive monitoring, etc. Do whatever it takes to get this experience, but don't get stuck without a job or in the wrong type of unit.