I recently wrote an email in which I wanted to thank to people and wrote
Спасибо болшгое, оба вас.
This was described as "scatalogical" by one of the recipients who suggested instead
Вам обоим, большое спасибо.
I am particularly puzzled by "обоим". Based on the use of "Вам", it's apparent that the suggestion uses the dative case, but I've never seen обо declined as обоим. Is обоим correct in the sense that a school teacher would have their students use it?
You seem to have interpreted спасибо as implying a transitive verb (by analogy with to thank) which requires Accusative case as applied to inanimate objects, kind of like
Благодарю [что?] вы (instead of [кого?] вас)
It just have to be memorized that спасибо alone corresponds with Dative case, probably because it implies the verb говорить (спасибо) кому?, so your phrase essentially means (Говорю) спасибо большое (кому? Dative) - вам обоим.
Oба always follows pronouns, like in English you both instead of both of you, i.e. вы оба; вам обоим, but precedes nouns and adjectives.
As a vehicle for memorization of the Dative case it's useful to treat спасибо as my thanks go TO.
HERE you can look up declensions. Make sure that the word is spelled correctly.
The rearrangement of the phrase by the addressee was unnecessary.
Firstly, both = оба, not обо.
Yes, the dative of оба is обоим: https://en.wiktionary.org/wiki/%D0%BE%D0%B1%D0%B0#Declension
So вам обоим is the correct expression of `to both of you'. I would put the original phrase this way:
