This is a difficult question because much of what we might talk about regarding the values and ideology of Romans before, say, 100 BCE is going to largely be based on sources written well after that period. This would lead to a certain circularity: for illustration, Augustus promoted moral laws in an attempt to recreate the moral values and practices of early Rome. We talk about the moral values if early Rome using, say, the histories of Livy. Livy was a major intellectual figure of the Augustan period, and thus part of the intellectual (and political) climate leading to Augustus' edicts. So you can say that Livy provides a source for the old Rome Augustus wants to return to, or that Livy's history is part of the same political moral movement as Augustus' edicts, that it is not providing a description of the past but a prescription for the present.

As should be clear I favor the latter interpretation.

That said, we can probably say that probity, fidelity, and familial piety were of great concern to early Romans due to what fragments we have of their legal practices. We do not, for example, have persevered the Twelve Tables, the earliest Roman law code, but we know enough about it to know that at the very least familial matters featured within it (seemingly not as much as tree related disputes, though). Perhaps more tellingly, one of the more bizarre punishments the legal system could grant, to be sown into a bag with a rooster, a dog, a snake, and a monkey, was given in cases of patricide (such threatened one of Cicero's first defendant, Sextus Roscius), the ultimate crime of infidelity and impiety. The nature of this punishment does seem to show that a particular significance was attached to crimes of the family, but going much beyond that is rather outside of our source base.

So the short answer is something along the lines of "probably to a point, but the context of the Augustan laws should be seen within an Augustan context, not a hazy one of early Rome".