First, it’s best not to have general anesthesia during the first trimester because the fetus is developing. At 3 months, your wife should be out of her first trimester or close to it (>14 weeks).
Next, let’s skip ahead and talk about the 3rd trimester. In the 3rd trimester the uterus is so enlarged with the fetus that elective abdominal surgery becomes more difficult. It’s best to do gallbladder surgery laparoscopically. With an enlarged uterus and baby in the way, no surgeon should really be doing laparoscopic surgery in the 3rd trimester, although there are always exceptions. The anatomy of the internal organs can also be somewhat distorted because of the enlarged uterus. Granted your wife has a gallbladder issue, but just to make a point, the appendix can be in the right upper abdomen in the 3rd trimester instead of the right lower abdomen. During the 3rd trimester, the weight of the enlarged uterus and baby also puts a lot of pressure on they inferior vena cava and can inhibit blood flow to the mother when she is lying on the operating room table and paralyzed, as with gallbladder surgery. A surgeon should place a pregnant patient titled on the operating room table to keep the uterus off the vena cava, but that can make surgery more difficult as well with the patient tilted, again another reason why 3rd trimester surgery can be difficult. Last, in 3rd trimester any strain on the mother could lead to pre-terms labor. General anesthesia and surgery is such a strain. The baby will also have to be under intense fetal monitoring during the operation with her OB doctor and many women will be managed by high risk OB doctors in the peri-operative period.
The 2nd trimester is best for elective surgery during pregnancy because it doesn’t have the same risks as 1st or 3rd trimester surgery. For the reasons I mentioned above. The fetus is for the most part all developed, ie the baby has its parts, it’s just all growing in size. And, there is room in the mother’s abdomen for the surgery to do their thing. In this case, the gallbladder can be done laparoscopically. I recommend you have your wife see a experience general surgeon to get her gallbladder removed soon. And like I said, it should be done laparoscopically, no need to do open, but of course I’m not the one examining your wife so that has to be taken in to consideration, in addition to her other medical and surgical history.
Hope this helps.