This must be hurtful for you and it does seem quite one-sided and controlling.
Perhaps your dp's daughter has issues with you or the conversations relate to relationships between dp, his dd and his X?
Not necessarily sinister, he may be avoiding discussing things that he may (even if he is wrong), think you you would find uncomfortable or may react to. Is there any chance this could be the case - at 14 she is at a difficult age? does he feel / is he right - that this could be the outcome? She could also be playing control games with you and your DP and he is being taken in as most Dad's are by their DD's
Re - his financial secrecy. Again this may not be anything sinister - but does seem controlling and whilst you call him your DP - this is arguably not the case as partners should not have (m)any secrets from each other in such an important area. Mildly sinister thoughts again relate to what is he actually paying to X (or his DD). Major sinister thoughts would be his has something worse to hide - undisclosed debts,gambling, substance abuse issues or other women?
You do need to talk to him about these issues individually I suspect - but very much start in a non - confrontational way - picking the moment carefully when you are both relaxed and on your own, so that he has no excuse to react defensively to you. this could start as..
Money
I am a bit concerned about the household money at the moment - as I was thinking we may want to be working / planning for buying a new car, going on holiday, moving house etc... I think we should have an account where all of our money goes into and bills etc are paid from and the suplus (hopefully) goes into a seperate deposit / savings account - we should each have / keep a seperate personal account which we transfer an agreed amount of money into each month from the main household account for us to use as we see fit.
He can then still have some privacy but not sufficient control of his finances (within the household / partnership context) that you could be left exposed to any problems.
If he is not prepared to do this - then I think I would need to know why?
Our kids
You are great in the way you give me such support on how to raise my son, I really appreciate what you do and the help you give and they way we work in partnership helping him grow up with such a good male role model. I am concerned that I do not seem to be able to give you and your DD the same support (especially if she lives with you most of the time). I do sometimes feel excluded from your relationship with her due to the - private conversations and texting- does she / is she (still) holding bad feelings against me? When she is part of our household and family I want to be able to support her in the way you support my son.
In truth I suspect that it must be difficult to have a 'partnership' when you are partially / largely excluded from two such central areas of your life together. If he has valid reasons for this - that you can accept - then that's fine but if not, then you need to find a way to make a change to this situation as you will increasingly resent / be concerned about these exclusions.
I hope this is helpful.