The answers in the question
I've worked shifts for years. 3 shifts, 4 shifts, even 5 shifts in the good old days. You will probably find there is a clause in your partners T&Cs along the lines of ...
"The company reserves the right to reduce or increase your hours of work and vary your shift pattern at some future date. At this time you will be given notice of the proposed change".
Oner of the pitfalls of working shifts I'm afraid.
A decent company will give appropriate notice (something similar to the notice you would be entitled to if you were made redundant) and recognise the extra hours by for example amending shift allowance or pro rata increasing salary (though they don't normally like doing that as it has implications for pensions, redundancy calculations and future pay calculations).
Your partners action depends on how financially worse off she feels she will be, how strong your union representation is. If you have no union represenation a bit of brainstorming will probably come up with a list of reasons why they should gie you an increase.
Extra hours (obviously).
Extra travelling time.
Extra travelling costs.
Loss of time off.
Loss of rest days.
Loss of weekends
try and put a financial element to your argument as well as a social aspect.
Also you may wish to look at the EU directive on working hours which limits the imposition of shifts which take the average working week to more than 48 hours (the average over a period of 17 weeks I think).
Hope this helps.
Chas