One of the best things you can do for her is to stop any self-blaming she might be inclined towards. Reassure her over and over again that none of us can prevent the behaviour choice of another.
One of the best gifts you can give her is to get her to establish a proper timeline for the affair and to recognise that there are two whole stages in affairs, before they start in earnest. These are the friendship/mirroring stage and the pre-affair permission-giving stage. The clock needs to start from first contact with the affair partner and not when the affair itself started.
The reason this is so important is that she might be believing that her marriage had hit trouble before the affair began and that this was causative in it starting. However, by that time, the die has usually been cast and nothing can stop an affair happening, apart from the dubious willpower of the two affair partners.
Whatever reasons your BIL is giving for why he had an affair, your sister also needs to recognise that affairs are never solely relational in cause. If they are to get past this, as a couple they need to establish why your BIL was personally vulnerable to infidelity and how his lifestyle and beliefs contributed to his decision to deceive.
In the aftermath of a terrible shock, there is also absolutely no motivation to pay bills, get uniforms ready and undertake too many practical tasks. It is as though the world has stopped turning. Remove as many of these mundane tasks from her, because that will help so much.
The other thing you can do is to have their DCs for a few sleepovers if you can, because as a couple, they are going to need lots of uninterrupted time talking about this.