I've always assumed the shabby house has more to do with lazy indifference than it does with lack of assets. Can't see Rob prioritizing redecorating his house over getting high and drunk. Not to mention, his idea of shopping for his wife is...writing a cheque.
As for Renata, she is apparently incapable of procuring her own cigarettes and diet Coke. Her parents apparently take care of the children most days. I'm guessing buying new furniture is probably a bit ambitious, never mind the effort and disruption involved in repainting walls and refinishing floors.
Taking it as true that Deco - and whatever other assets (e.g. real estate) - were worth some millions prior to the death of the father, it is a virtual certainty (as in, 99.9999999%) that the father had an estate plan prepared for him.
By far the most common plan is one by which (1) Deco - and whatever other assets - would be lodged in corporations whose shares in turn are owned by a so-called holding company that was owned by the father, (2) the shares of the holding company would be placed in a so-called family trust, the trustees of which would be the father and one or two or three other people whom the father would expect to 'do what he would do' after his death - such as the mother - and (3) the terms of the trust would give the trustees discretion about what to give to the kids from time to time (including to give some of them more than others). The father's will also would provide that whatever property might pass by his will (rather than being in the family trust just described) would be held by trustees for his estate (probably the same people) on similar terms (and, IIRC, it was said by some source that the estate of the deceased father made a loan of something like $5 million to Deco, which would suggest that the total value of the estate is more than $5 million).
The end result is that, on his death, most of the father's wealth would be held by the family trust (and, therefore, would not pass by his will, and so would not attract probate fees - what people call 'death duties') and any other wealth he had would be held in trust under his will. Therefore, aside from salaries paid from Deco to the kids (it seems, as of now, only Randy and Doug Jr.), the income generated from the assets that made up the father's wealth would flow through the family trust and (to a lesser extent) the trust under his will. The trustees would be quite able to put Rob, and by connection to him Renata, on a more modest 'allowance' than is given to the mother or to Doug or Randy, or even to Kathy.
I suspect (but can only suspect, of course, because the terms of a family trust do not have to be filed anywhere public) that the trustees are the mother, Randy (despite his history, he is the eldest kid, and he passed the lie detector test) and Doug, and perhaps a fourth person (such a the father's lawyer or accountant - not Hotmail lawyer, or I'll eat my hat) and that Rob, and by connection to him Renata, are kept on a short lease (in $$$ terms) because they cannot be expected to manage money wisely.