You apply for the Non Immigrant O visa based on being over 50 years of age, this visa gives you 90 days of stay and during the last 30 days of that stay you can apply at Immigration for the Extension of Stay based on being over 50 years of age.
Your wife can apply for the Non Immigrant O visa based on being dependent of an alien with a long stay inside the Kingdom, this visa gives also 90 days of stay and during the last 30 days she can apply for the Extension of stay based on being a dependent of an alien with a long stay inside the Kingdom.