Question

William and Mary were offered the throne of England to?
improve relations with Holland.
prevent succession by a Catholic monarch.
stop Parliament's rule.
restore the monarchy.

Answer 1

Well, the second is probably the answer that's wanted, but it's kind of screwy. In fact, England already had a Catholic monarch in James II, and before that in his brother Charles II.

The problem is more that James was attracted to the model presented by King Louis XIV of France, of absolute monarchy and Catholic purity, untrammeled in the first case by the painful concessions on divisions of power worked out between King and Parlaiment during the Revolution and Restoration, and upending in the second case the painful compromise of toleration that had been the result of the long struggle between the Church of England and the Nonconformists.

In short, James II seemed to want to upset the applecart, and undo the compromises that had made the powerful opposing forces in England come to uneasy accomodation with each other. Furthermore, he was strongly suspected of wanting to put England in thrall to the Sun King, which no Engllishman could stomach. Hence the fact of the birth of his son (which was controversial -- there were some who believed the child was an imposter) was probably in some case a pretext, or the straw that broke the camel's back, for the invitation to William and Mary to take the throne of England and the revolution of 1688. The underlying cause was probably James II's drift towards absolutism, Catholic purity and subservience to France.