Replacing coat lining

My daughter has this fabulous long black coat - she looks FABULOUS in it - like a Russian Princess - but the lining now has to be replaced. I can't afford to buy another coat like this (just lucked out and bought it on sale 3 years ago)

The style is classic - I want to replace the lining with a heavy satin lining.

I have some sewing experience - I assume that I carefully remove the lining - then separate each piece and use them as the pattern pieces making allowances for seam edges - then re-attach the lining.

Has anyone actually done this - and what headaches should I prepare for?

thanks in advance
Michaela (aka SE-andor)