Thanks for sharing the question. A mini lift will help lift the jowls and some of the vertical lines outside the corners of the mouth. Neither the surgery or facial lipo will widen or pull the mouth. Even most facelifts will not "pull" or "widen" the mouth. You may need to speak with a surgeon to discuss other possible options. Best of luck melaniene!
A mini lift usually applies the vector superiorly on deep tissues and superolaterally to the skin. The effect is minimal on widening of the mouth.
Facelift, or a minilift will not change the appearance of the mouth itself. The lateral deep lines, marionette lines and nasal labial folds are reduced with a proper facelift or minilift, but the mouth and lips are not changed. Fillers to the lips or corners of the mouth can reposition slightly the position of the mouth and should be an easy first consideration for alteration of the mouth position and alignment.
The mini-facelift and facial liposuction that you are scheduled to undergo will not help widen your mouth. The mini-facelift will elevate and tighten your jowls and to some extent help with some upper neck skin laxity. Widening or enlarging the mouth is not something that you can expect from the procedure.