If she needed a man to latch onto for security alone, she should have found it in a successful closeted gay Hollywood costume designer and married him. Or maybe Liberace, who was at his peak popularity, and all the world was abuzz on when he would finally marry.
In such a sham marriage, she could have had all the "cousins" she wanted. Problem solved.
Indeed, Liberace was at his peak when the film was made. My lady friend of the time talked me into taking her to a concert of his in San Jose, California, in 1953.
Life, every now and then, behaves as though it had seen too many bad movies
No, she didn't want "security." She wanted a real--if unrealistic fairytale-- kind of love. Movie stardom had already given her security, in a financial way. Even when confronted with her husband's incredible deception, she thought she could continue her fairytale by giving him a child, so that his family line could continue.
In the unlikely event that her husband would have accepted such an arrangement, I rather feel she wouldn't have had any more "cousins." Of course, she didn't have a chance to tell him. (In Italy, in those days, the hubby probably escaped imprisonment, or was out soon--a "crime of passion," and all that. It doesn't seem that Bogart told all, so Ava's character took the rap for being a slut, and justifiably dealt with.)