@pontipinemum
I'm so sorry you're going through this.
One of the things I've learnt with DH is that alcohol can turn even the most truthful person into an inveterate liar. DH was one of the most honest men I'd ever known, but now if he told me it was raining I'd go look out the window. And chances are I'd find a sunny day.
And it's not just drinking they lie about. For whatever reason it seems that their first reaction to any question, even something as simple as "Do you have milk in the house?" is to lie. It's just so disheartening. But there's no point in saying anything to them, because they'll just lie that they've been lying. All you can do is murmur 'Mmmm-hmmm' and change the subject unless it's something you must respond to as it affects you directly.
I can't say I blame you for checking her emails, especially wrt things that may affect you or affect her finances. Ignorance is NOT bliss when it comes to something that could hurt us, or that we'll be called upon to bail the alcoholic out of. As far as I'm concerned, the end justifies the means.