Smart Lipo or Mini-tummy Tuck?

This is best answered at your consultation with your Surgeon. A physical examination will evaluate your muscle anatomy to your abdomen that can sometimes be affected by pregnancies, widening the center of the rectus muscle that runs straight down your abdomen and this may cause a projected abdomen. This can only be repaired with a formal abdominoplasty because the plication, or bringing together, of the rectus muscle is done above and below the naval. The amount if fat that lies above your abdominal muscles will also be evaluated to determine if liposuction is appropriate and would give the results you want. Sometimes, weight loss and exercise can be an option too! You may not need a mini tummy tuck with the description given, but again, a physical examination is necessary. 

Thank you for the question.

Without examination or pictures is not possible to give you accurate advice.

However based on your history, in general I do not believe that you will be a good candidate for liposuction surgery.

Also, in my opinion, the mini tummy talk is an  operation that  produces very limited results and is very rarely indicated. It involves a shorter incision but does not address the majority of the abdominal wall issues present for most patients who present consultation. For example, the area of skin excised is quite small. The abdominal wall musculature is addressed below the umbilicus leaving the upper number wall potentially lax. The appearance of the umbilicus is not necessarily addressed sufficiently.

For most patients who have had pregnancies and/or weight loss a full abdominoplasty is necessary to achieve the desired results. Of course, there are downsides (including a longer scar and probably a longer recovery time) but for most patients the benefits outweigh the downsides. It is not unusual to see patients who've had mini tummy tuck  surgery present for  revisionary surgery.
It is important to work with a well experienced board-certified plastic surgeon to obtain advice (based on good ethics and judgment) to  improve your chances of a successful outcome and minimize the need for further surgery.
I hope this helps.