I do agree that vinyl is prone to pull away from the stiches. But the right kind of interfacing can help.
Upholstery vinyl is often backed with a cotton mesh which can help, as well.
For corsets I would recommend coutil interfacing, stitched in (also called flatlining). I would not recommend satin lining for any corset. It is too slippery, and a corset needs to stay in place. Cotton flannel is a great absorbent, comfortable lining that will stay put. Also, I have seen at some Renfaires a pattern for a corset/bodice that is one piece. Since vinyl has no grain, and seams will only weaken it, this may be your best bet to develop a one-piece pattern. The flatlining and lining should have seams and be cut on the grain to control any possible stretch. Stitch the flatlining together into one piece, then stitch to the vinyl around the edges.
For vests, any thick cotton lining will work, sewn in as flatlining. Again, reduce your seams as much as possible.
You could invest in a small craft iron. They have a little hot point that allows you to only apply heat to small areas. You might sandwich your vinyl and fusible interfacing between cotton press clothes, and apply this small craft iron only around the edges. Or you can just buy fusible tape, and fuse it to the inside of the seams after they are sewn as reinforcement. As an alternative to heat, you might use fabric/craft glue to glue reinforcement tape to the insides of the seams. Decorative trim glued on the outside off the seams (particularly on the corsets) might work as well.
I would not recommend vinyl for cloaks. It does not drape as softly as leather, and would look horribly modern. Also, baglining or flatlining a cloak almost always leads to a sagging lining that just looks messy. Consider ultrasuede fabric as well, it's made of polyester, looks and drapes like suede, sews easily, wears well, and is relatively inexpensive. Also sold in the home decor section. Ultrasuede makes good vests and bodices as well, and an extra benefit of a cloak in ultrasuede - sueded or brushed microfiber is a bit more expensive, but also looks a little like suede and is water repellant.
Ultimately the wearer will want to reduce all possible stress on the seams, which means wearing the right size, getting a good fit, and just not wearing something too small. To insure this, you might consider stretch panels under the arms.
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