Thanks for posting your pictures. You have a very large rectus divarication, and the skin just above your umbilicus is damaged. What happens is that the fat under the skin splits apart, leaving your skin without the normal thickness of fat underneath it.
It is repairable though I think, and I would not recommend a vertical scar. A conventional tummy tuck should do well, and once the muscle repair is done there will be plenty of loose skin to enable a low transverse scar only.
One important thing to add though: you might well need a scar revision of the low transverse scar 6 to 12 months post procedure to achieve the best result. The damaged upper abdominal skin after what was clearly a really big pregnancy won't look really smooth just above the scar initially. Over time it will get better, and if it needs a touchup later onto achieve the best possible scar, in my opinion that's a better option than a vertical scar. Any touchup would've minor in nature and recovery.
This is a good question. Some surgeons feel they need to add a vertical scar in to a tummy tuck to achieve the best shape. The problem is, the operation is supposed to make your tummy look better! So the burden of a new scar there if there was not one there before is a significant detractor from the appearance.
I am not a believer that a vertical scar is necessary. Over 20 years and with a large tummy tuck practice ( more than 50 per year) I have used a vertical scar no more than 5 times.
Of course, without seeing your pictures I can't be certain - I have seen the skin around the belly button so damaged that all you can do is remove it, but that is RARE.
The aim of a tummy tuck is to restore trunk slimness, smoothness and the integrity of the muscle wall, with as inconspicuous a scar as possible. Often the scar is long: but if it's low and transverse, then underwear will completely disguise it, and no visible scar should be evident.
If the skin is thin, adjunctive measures such as fat cell grafting can be used to restore the thickness.
My advice would be to seek at least another opinion, or talk to your PS about alternatives to the vertical scar. And consider posting some good quality pictures on realself, where our advice can be much better. YOu won't be identifiable!