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We'll probably need a clearer, more detailed explanation of exactly what you're trying to accomplish. Is one of those an example you're trying to replicate?
As I (mis)understand it, you can use the Corner Widget if applicable,
or you can use the free Round Any Corner script by 佐藤浩之 Satō Hiroyuki (just scroll down to it),
Try deleting that extra point on the Palatino S with the minus key, shift-C the end point to build a bezier curve. There's probably a key to build only one side of it - but I don't know it (anyone?) - so just collapse the unwanted side back to the point's apex.
Here I started with Palatino LT Std, Roman as you suggested.
Next Type>Create Outline
Select your S, then switch to the Direct Selection Tool (white arrow) to reveal the Anchor Points.
Select those two Corner anchors and convert them to Smooth anchors.
Slightly adjust your handles.
Did you try to use Simplify Psth option from Object-Path menu?
Google says: Designed by Hermann Zapf for D. Stempel AG, this typeface was originally intended to be the book or text weight for his Palatino font family.