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VERY loosely translated (with some guessing):"I'm glad it seems that [missing subject] was not angry at all. I don't think you have to worry about the late-shift/overtime on Sunday. Man, you're so lucky!"

Ok so...I'm just running around the internet randomly translating stuff.
Also, I apologise in advance, my Japanese is rather shoddy BUT...I think I can do a little something.
One more thing: Was this originally a written message and did you actually receive this message in Romaji (i.e. Roman characters) or were there cool Kanji too, 'cause that would help me to translate a LOT. Right...and now WHY I translated it this way

First Part:
zenzen okotte nakatta mitai--it seems that [smn.] was not angry at all
yokatta desune--that's great/I'm glad/good for [you]

zenzen=totally, completely [or "not at all" in the negated form here]
okotte=okoru=to be angry ["-te" form is used here to pair it with the negation~]
nakatta=nai=[here]to not be/is not["nakatta" is atattched to the infinitive or "te" form of okoru to describe a past condition or development]
mitai=(adj. suffix) seems like/looks like
yokatta=yoroshi=good(fortunate)[again, "-katta" form to match with the whole "past tense-edness" of the statement]
**note, Japanese has a habit of dropping subjects from sentences when the subject is understood so there is in fact, no subject in this sentence so we don't know "who" was "not angry" but, you should.
[certainty 95%]

Second Part:
Sunday no osoban [no koto]--[regarding/as for] The late-shift[?] on sunday ["regarding"...really a supplemental structure required by Japanese, can be ignored in translation]
mo zettai kizuite nai hazu desu [si]=[it also] seems like there isn't a lot[?] **"the "si" in "desusi" is a form of inflection that I am not familiar with or may not exist...

Sunday=...
no=possessive/descriptive particle=of/the...of.../...'s
osoban=late-shift (as in a job)[partially guessing on this one...]
mo...nai=not...either/there isn't either
zettai=lit. absolutely=not at all (with certain verbs (modals?))
hazu=inflection suffix=it seems/I guess/It should be this way
desusi=desu=your standard Japanese copula which acts as the verb "to be" but really is more like a particle establishing what came before as "a statement"
**desusi is not a form of inflection I'm familiar with, regardless it does not affect the translation here
[certainty 70% this whole part hangs on the main verb "kizuite nai" there is a verb "kizuku" which means "to pile up" so...not sure]

Third Part:
Datte=means a lot of things as a conjunction, but here I think it's being used more as an interjection like: Man/jeez/wow...
urayamasii desu= lit. [I] envy you=you're so lucky
[certainty 99%]
Of course...this was like a week ago, so you either got an answer somewhere else, or the issue is thoroughly moot by now, oh well!

desusi is another way of writing desushi, or ですし. In this context I believe it can be translated to "etc", "and so on", etc.

anyway, you did an awesome job explaining the translation!