Is the wife sinful for refusing her husband's request for intimacy after the Adhan if that would lead to him missing congregational prayer?

It is not permissible for a wife to refuse her husband's bed unless there is a legitimate excuse. It is permissible for a husband to have intercourse with his wife after the Adhan if there is sufficient time to catch the congregational prayer. The default rule is permissibility unless there is evidence to prohibit it, and the matter is conditioned upon attending the congregational prayer in the mosque because it is obligatory for men. If intercourse will cause one to miss the congregational prayer and there is no dire need, then prayer should be prioritized, and the wife incurs no sin for refusing intercourse at that time. An exception to this is if time is short and the man's heart is preoccupied with intercourse, such that it is feared he will not have full devotion in his prayer. In this case, intercourse is permissible and may be prioritized over prayer, even if it leads to missing the congregation. This is analogous to someone for whom food is served or who is greatly pressed to relieve himself (defecate or urinate), due to what occupies the heart and diminishes the perfection of devotion.