What was the Sadducee attitude to the Roman rulers?

Answer 1

It was likely one of obsequiousness and trying to curry favor.

The Sadducees were men of politics and secular life, similar to the Hellenising Jews. They had abandoned various parts of Judaism; and they claimed no earlier source or tradition for their attitudes. They harassed the Torah-sages; and, like the tiny breakaway group called the Essenes, dwindled away after the time of the Second Destruction, like the earlier Jewish idolaters after the First Destruction.

Note that there is a common misconception that the Sadducees, like the much later (and now largely defunct) Karaites, made a deliberate decision to reject the Oral Law and reinterpret the Scriptures.
However, a careful perusal of the Talmud reveals that the Sadducees were actually opportunists who had nothing much at all to do with religion in any fashion. They were lax in Judaism and had little interest in Torah-matters.

At that time the Jewish courts still had the ability to enforce the Torah laws, and almost all Jews were Torah-observant; so, in order to avoid total rejection by the surrounding community, the Sadducees outwardly maintained a facade of keeping the major Torah precepts (such as the Sabbath), while simply ignoring the Oral Torah and customs.
They went lost not long after.
The group that did (on rare occasions) debate against the Torah-Sages concerning subjects of religious observance, were a tiny sect called the Baitusim (Boethusians), who quickly died out.

See also:

Other ancient groups