According to the death index her DOB was 24 Dec 1921,so you will not find her marriage.....from 1941 onwards I would think,on Free BMD.
You will need to trawl through the pay per view COMPLETE indexes 1/4 by 1/4 .
The same will apply to finding any children.
With a name like Green I don't envy you,it's not impossible,but you'll need plenty of time and plenty of coffee

I think a few questions to other family members may be the best way to go here.
Carol