"I work a total of three weeks."
Translation:Jag arbetar sammanlagt tre veckor.
Jag arbetar sammanlagt tre veckor. only means that you work at at a place for a total of three weeks (and not more than that).
If you want to say that you have just started a new job and have been working there for three weeks so far then you'd have to say Jag har arbetat här i tre veckor and if you want to be more precise then Jag har hittills arbetat här i tre veckor.
Sammanlagt = (Something) put together to form a total amount (But not put together as in fixing something that is broken or putting together a puzzle)
Hittills = So far
I couldn't say if it is more idiomatic to say this sentence in that way... But if you take a look at the tips and notes section added on the first skill of adverbs you will read this: Unlike English, adverbs are always placed after the verb in sentences that start with the subject. This is because of the V2 rule – the verb must always come second.