Frank (book & show) is so boring and creepy to me. The Wakefields aside I found the 40s segment dull for the most part. I hope we will not have to endure a 20th century segment in every episode. I just can't with Frank. I never found it very believable in the books that she stayed married to Frank for years after her return. I think she had already started to outgrow him before she went back in time. Is she going to have an ongoing sexual relationship with him? It was hazy to me in the books whether they returned to having regular marital relations, shared the same bedroom etc.
The heroine who can't get pregnant by her husband because he's sterile is a common romance novel trope. I suppose they had Frank knowing he's sterile this early on to make it more believable that he would raise another man's baby as his own( not ever wanting said baby to know the truth). I know book Frank before Clare went missing was opposed to adoption and had no interest in raising a child who wasn't his own blood. I always thought if Clare had not gone back in time this would have been the thing that broke them up along with her outgrowing him and finding life with him stuffy and boring.
I don't believe book or show(so far) Frank believes Clare. I don't think he believes she's making it up or willfully lying. I think he thinks something happened to her that was so traumatic or she did something she feels so guilty about her mind has made up this story to keep her from having a complete mental collapse.