Congratulations on your weight loss! After pregnancy stretches your abdominal muscles you have a diastasis, and occasionally an umbilical hernia. True ventral hernias are more uncommon, but can occur. This would mean you actually have intra-abdominal contents (intestines, colon, or omentum) protruding outside your abdomen into the subcutaneous tissues, much like a weak spot in an inner tube. This warrants surgical repair to avoid stangulation of the bowel and peritonitis.
A small "outie" belly button is NOT a ventral hernia, and if your surgeon is telling you s/he can obtain coverage for hernia repair so that you can have (part of) the operating room fees and anesthsia costs "covered" by insurance, this is "stretching the truth" at best, and insurance fraud at worst. You could get stuck with the entire hospital bill, which will be thousands more than paying for what you really need and want, which is a tummy tuck with muscle repair.
The surgeon asks for separate payment "on the side" for the "cosmetic" part of the surgery. But your basic charges at the hospital (OR, anesthesia, etc.) are all billed at the (much higher) hospital rate, so even the "self-pay" portion of the operation can end up costing more than if you paid for the entire tummy tuck procedure (and skipped the attempt at coverage) by a reputable ABPS-certified plastic surgeon who will repair the hernia and diastasis as part of the cosmetic tummy tuck operation you actually want/need.
You do not have a pannus (by your description of a "small amount" of loose skin of the lower stomach), and panniculectomy is the wrong operation anyway, even if it IS "covered" by insurance.
Read Dr, Aldea's answer as well as the other answers here. Also, check on the credentials of the surgeon who is recommending this plan--I am concerned that s/he is not an ABPS-certified plastic surgeon, or has questionable ethics that might mislead you into either the wrong or an incomplete-result operation, inadequate tissue removal and need for another (self-pay) re-do operation, and/or a much more expensive than anticipated operation when all the bills get added up.
See a few more ABPS-certified plastic surgeons and get an idea who is telling the truth here. You deserve a fabulous result after all your hard work, even if it does cost a bit more up front. Factor-in the costs (not only money but time off work and repeat risks) of secondary surgery to get things right, and you see why we're concerned about your question and the "plan" as outlined. Best wishes! Dr. Tholen