Sylvia seemed scalded it had all happened IN FRONT of her mother,

Yes, particularly since Plath had represented the marriage in such a rosy light to her mother in all those letters.

Have to wonder what might've happened if she had gone home even for just a visit and seen her psychiatrist or maybe another doctor....

Yes, if she'd been able to see that psychiatrist she liked, it probably would've made a difference. Heck, if she'd managed to avoid that giant London blizzard, she probably would've made it through...