A certain amount of private expenditure from the "domain purse" is not merely possible but expected, it's when the regent overdoes it that you get issue (each domain drawing the line of acceptability in a different place).
One of the things I always find amusing in PBeMs is that nobody "wastes money", where is the construction of the massive townhouse, the great statues and art, the opulent tombs? A lot of people earned money in the medieval world to spend it, not to invest it ;-)
I note that it isn't just rulers who occasionally have to flee either; some guild hostile takeovers can get nasty, and the in-fighting in some organisations could be brutal. In BR of course most "GB" aren't portable, but even so a "secret stash" could exist in any domain in my view - it's a pity that the Conclave's 100 GB stash and its history was missed by most of you - it was beautiful.
The great statues, the art, the opulent tombs, the massive townhouse is IMO all found in the context of other actions. Rule holding could have a description of the erection of great buildings with no effect on domain play.
Agitate actions, festival (grant) actions and so on could be used to describe great statues and art.
If I at some point use GB effort on an action where it might be appropriate I could describe in a building, statue or other piece of art.
As I see it there is plenty of room to give your regent what he want, within reason, without "wasting money". The other characters in your domain is paid by your domain upkeep, and as such must have a personal treasury they can use as they see fit.
Please tell me if I am way off base.