You want a huggy bear coat
So, fur outwards. Yes ?
Most fur coats are made from fine skinned furs and they are pieced from small bits. If you can unstitch the lining from the best one that will fit you….sort of fit even….then have a look at the inside and see just where you might need to split the stitching to add in extra.
Measure up the parka you want to use as an inner and make sure that you have enough fur to go around it properly. If you have to cut the fur then the best idea is a razor blade on the skin side and then just gently pull once you're through the skin. You'll lose a lot less hair that way and you won't have half cut ones either from using scissors.
If the skins are sound then you can simply stitch the two together at the neck and front facings and at the cuffs. I reckon you'd get away with leaving the hems with just a couple of tether bars (think of using soft ribbon rather than stitching cords with blanket stitch, it'd be gentler on the fur I think) at the side seams.
Stitching the two together….the biggest issue is that you don't want the thread to cut the skins, but you do want it to securely hold the two together.
If it were me, then I'd use fine linen thread and small stitches, but then, that's me and I'll stitch fine anyway.
I 'think' it'd be fine if you did vertical rows of running stitch down the length of the two pieces to hold them together…think quiilting like on an duvet. If you can manage to do join the front edges with a whip stitch then that would support the fur and hold it snuggly against the inner cotton jacket. The same should work at the neck and cuffs.
You're going to look like an animated teddy bear in this though Chis
Sue'll want to cuddle in
M