The vast majority of board certified Plastic surgeons were trained and certified in Surgery before training in and certifying in Plastic surgery. As such most of us are very comfortable repairing ventral and umbilical hernias.
We often CHOOSE not to do so and bring in a General Surgeon in these cases for a variety of reasons foremost of which is to allow the general surgeon to repair and bill for the often insurance covered part of the case (hernia repair) while deflecting potential liability for it. Had we not lived in such a sue-happy society, a lot more would be done for a lot less and we would all benefit.
As far as your options, you can choose to have nothing done. You can choose to have your umbilical hernia repair and stop or have your tummy tuck a few months later. Finally, you can have your hernia repaired at the same time as your umbilical hernia repair. Without any health risks you have not told us, that would be my preferred way of approaching most such cases.
In your case, you appear to be obese. Your risk for complications is higher including loss of the umbilicus (due to a poor blood supply to the umbilicus which would be poorer after the hernia repair). But, your potential functional and appearance benefits are far greater.