You see, if he was truly mortified at having been found out at the way he's behaved, then you shouldn't need to "work" at getting your name onto anything .....
.... HE would have immediately sat you down, apologised profusely, begged your forgiveness, and shown you everything - so you didn't have to wonder how much is in that particular savings account for example. HE would have immediately offered to put all savings/investments into joint names, and, initiated a discussion with you about how finances will be dealt with from now on in, e.g. completely combining all income sources, paying all regular bills, deducting any occasional expenses due that month, and then equally dividing up what's left so you BOTH have the same amount to spend. HE should have also, in the circumstances, immediately offered to make it up to you and the kids in some way for all the years you've been (needlessly) missing out. HE would also give you the passwords for anything online so you're never left in the dark again.
He hasn't done that has he ? :(
He's kindly donated £1800 ..... which I think is him buying time TBH. The house budget thing is okay in itself but misses the overall point. The offer to replace CB lost next year is hardly being over generous since no doubt it'll be spent on food, school stuff etc anyway.
I think he's trying to keep you sweet, at least for the moment, with as little as possible. You are married FFS ... whatever happened to what's mine is yours and vice versa ? He may appear to be apologetic but he's still controlling the finances isn't he. He's still giving away - both literally and figuratively - as little as he thinks he can get away with. You may find that while you're still very cool with him that he'll "offer up" something else to bribe you with - such as this weekend, but after such a prolonged and calculated campaign of being selfish, being very ecconomical with the truth (at best) and of treating his wife and kids as second class citizens less worthy of having family money spent on them than he is, the only satisfactory solution to all this (and even then, I don't know if it would be enough for you to forgive him and move on, because some betrayals are too big) is TOTAL financial equality.
The important thing to keep reminding yourself of here is WHY - if he's apparently such a "fool" and wants to stay married - has he NOT instigated that equality which is long overdue and which you undeniably deserve ? I mean, why not ? What possible reason can he have for not doing this if he's serious about what he says ? ............ ah yes, he's hedging his bets, he still sees that money as "his" and his alone (probably thinks he's doing you an immense favour by throwing you a few crumbs), and worst case, at the back of his mind, it's a running away (at some point) fund.
Frankly a weekend away wouldn't do it for me. A weekend .... when, if you sat down and worked it out, you and the kids have probably lost out to the tune of thousands over the years while he's been indulging his penchant for designer gear etc. It's a bloody insult really. A weekend comes after you've sorted out what is very fundamentally very wrong ..... not before, because the underlying problem will still be there.
I mean, just how bloody long do you have to wait before he mans up over this ? ........ and even then, I still think you'd need counselling big style to come to terms with what's been going on, and to deal with the hurt and betrayal. You shouldn't have to nag, beg or manipulate him in order to put things right. All that should come from him - except it hasn't. I'm so very sorry for you because his heel dragging says it all really ...... if I were in your shoes I'd be starting to think it was ultimatum time: full disclosure, full access, equal division NOW, or else you instigate separation/divorce proceedings. And make it clear that when those issues had been righted, the future of your marriage still wasn't guaranteed as you need time to decide if you can come to terms with what's he's done.