You have good insight on some of the factors which contribute to your double chins. Liposuction of the fat, under the chin generally produces spectacular results if you are younger, male and close to ideal body weight. If you are heavier than you should be (consult the Body Mass Index charts on the Internet), you should try to loose some weight, because as the fatty component reduces, the overlying skin shrinks, slowly, producing a more defined chin-neck relationship.
The placement of scars for a necklift in men can be somewhat tricky. Assuming that you loose the extra 20lbs and are left with a lot of skin laxity, it's unlikely that liposuction alone will redrape the skin satisfactorily. There was an operation described in which the excess skin was cut off the front of the neck, in the shape of a "Z". I've seen a few older men, who had this procedure and the scars healed well, but it still looks like Zorro slashed them.
If you have a necklift, similar to your mother's, your surgeon should notify you that you may have to shave the bony area behind your ear, as the beard bearing skin is lifted and tucked behind it. I generally request all facelift patients to let their hair grow a little to camouflage a facelift or necklift, while they are healing. After the scars are "mature", you can restyle. Good luck.
