I can understand how worried you are belinda but I don't think that hiring a private investigator would help the situation - if your DD found out you had done it could damage your relationship with her irrevocably.
Certainly you need to speak to her, it is very strange that she doesn't know exactly what he is doing all day on his computer; if he rarely goes out then I doubt that he will have another family hidden away somewhere.
He could well be running his architectural business from home, but surely that would involve a lot of going out, meeting clients etc. It can be extremely difficult to get money out of clients and many a small business has ended up going bust because of cash flow problems. If he is not insistent on staged payments then this could have happened and he has tried other ways and means to try to make money.
Online poker, share dealing on line, bitcoin gambling - all good be lucrative or equally could lead to enormous debts which he is is struggling to repay and is reluctant to tell your DD about.
Your daughter needs to be more assertive in finding out exactly what is going on. Do they have a joint bank account or does she have her own? Whose name is the house in? You say her salary is enough to keep them - lots of people are managing to do just that without the luxury of flights, holidays etc, so explain to her that you are there to support her but not financially.
Would it be possible for you to have the children a couple of days a week so that she doesn't have to pay nursery fees for those days or are you still working yourselves?
If you feel you do need to support her, perhaps you could buy the children clothes and shoes - but not hand over money.
You need to speak to your DH and to your DD or else this could just go on indefinitely and you could end up with an impoverished old age yourselves.