I assume that Miles and Jesse are the sons of Mae and 'Tuck' - that's what they said, right? But Jesse called Mae by that name when he came to Winnie's window - why would he not say "my mom" ... I'm confused.
You give me joy that's unspeakable, Jesus I am so in love with You
they are from a different era. Would you really call your father by your last name, as they referred to Tuck (The father)
Jessie was born around 1800-1815 ish, if he was really 104 (if they didn't loose track of some years somewhere, which would make him older or younger).... in that era, maybe it was common to call your parents by their first names (or last)...
Or maybe in the past 80 years they had grown tired of saying mom (being that they only spoke to family) and just started saying mae instead.
I think the last theory is right, that they're tired of saying mom. Some families have strange names for each other, like Bart Simpson always calling his father Homer instead of Dad. (It's funny that the Simpsons and other cartoon families seem to have Tuck immortality but aren't upset about it!)