Will my 2003 arrest not allow me to get her visa approved?

Although not entirely clear from your question, I presume you are asking whether a U.S. citizen is disqualified from sponsoring a spouse for immigration benefits based upon the U.S. citizen having an arrest in 2003 that was dismissed, and having a separate 2003 offense under section 647(b) of some state's penal code. Generally, a U.S. citizen's own criminal history will not stand in the way of eligibility to sponsor a spouse, but for a legal analysis further information is needed (for example, Section 647b of the Penal Code in California relates to the offense of prostitution, but Section 647b of some other penal code may refer to an "Adam Walsh" type of offense with potential immigration-related consequences]. Of course, many other details determine eligibility too. There really is no substitute for you and the relative you wish to sponsor 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.