Surgeon here — we'd proceed with MRI if feasible. If she spikes a fever or peritoneal signs develop before imaging, take her to OR. The risk of perforated appendicitis to the fetus is far greater than the surgical risk.
MRI is the gold standard here and worth the wait if the patient is stable. Don't delay if she deteriorates. Laparoscopic appendectomy in the 2nd trimester is well-tolerated — open port placement slightly higher than usual to account for the uterus.