Fact: Your husband is a naasty, selfish, cheating arsehole who doesn't give a shit about you.
YOU KNOW THIS.
You do not need to have this proven any more, in order for you to take steps to protect yourself and your children.
Yes, you will need to be armed to confront him - absolutely. But that's different. For yourself, your peace of mind - you already know. YOU KNOW!
So yes, get proof if you can, to confront, etc. But for yourself and your future - you are beyond that step, aren't you? So you can start to take action.
-proof of his earnings and any pension etc.
-access to bank accounts. Joint money? - can you get hold of it and keep it safe from him?
You are married, so you have rights. But do everything you can first to secure finances - access to accounts, and information for child support/divorce.
I know you won't want to think of these things right now but DO.
Others have suggested getting proof through her phone - would that be possible? You work together? - could you 'get your phone wet' or run out of charge, ask her to unlock hers and dial x number for you (bank is good, say you've had a weird charge and you need to see if someone's cloned your card?) - ask if you can borrow her phone and then get yourself in the loo or somewhere - even if you have to run for it! - and then get to her messages. Have YOUR phone with you so you can take pics. It might work very well if she totally doesn't suspect.