He had intercourse with his wife when she was making up a Ramadaan fast. What should they do?

Praise be to Allah.

Firstly: 

It is not permissible for a person who has begun an obligatory fast – such as making up a Ramadaan fast, or offering kafaarat yameen (expiation for breaking an oath) – to break that fast except for a legitimate reason such as sickness or travelling. 

If he breaks the fast – whether that is for a valid reason or not – that fast still remains an obligation that he owes and he has to fast another day to make up for the day when he spoiled his fast. 

If he broke his fast with no excuse, then as well as making up the fast he also has to repent to Allaah for doing this haraam action. 

Your wife does not have to offer any expiation, because the expiation is only required for intercourse during the day in Ramadaan. 

We have previously discussed this in the answer to question no. 49985. 

Secondly: 

You did wrong by spoiling your wife’s fast, because if a wife observes a fast to make up for a missed Ramadaan fast, with her husband’s permission, he does not have the right to spoil her fast. 

You both have to repent to Allaah, regret what you did and resolve not to do it again. If you forced her then there is no sin on her. 

And Allaah knows best.