In order for us to apply for immigration, do we need to be married again or will they accept the Saudi marriage certificate?

Generally, the USCIS will accept a marriage as valid if it was legally valid where it took place. In the application process a foreign national should be prepared to show an original or certified copy of a marriage certificate, and if that document is not in the English language, then it must be accompanied by (1) an English translation, and (2) a translation certification. Neither the translation nor the translation certification needs to be from an official translator, but instead may be from any adult who is familiar with both languages and capable of confirming the accuracy of the translation. The certification may be signed before an ordinary notary public. Note, however, that it is impermissible to enter the U.S. with a visitor's visa while intending to adjust status to become a Permanent Resident. The reason for this is that use of a visitor's visa requires "nonimmigrant intent," i.e. an intention to remain only temporarily and then depart. Misuse of a visitor's visa can have very harsh immigration-related consequences. It would be wise for you and your wife to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.