I wrote the according to me correct answer, than I deleted it...

- but it´s ´must have´ not ´must of´ - you´ve been in Turkey too long!!!

Annem ayrılmış olmalı. (a guess)

Annem ayrılmalıydı. (expectation or advice)

So please enlighten me how you can translate these sentences to English. These translations will also answer your questions.

Well - it´s a guess or an assumption - so I guess the first one is correct! (although I still don´t see why ´ayrılmak´ rather than ´çıkmak/gitmek´

 çıkmak/gitmek is also ok.

Annem ayrılmış olmalı. (a guess)

My mother must have left.

Annem ayrılmalıydı. (expectation or advice)

My mother should have left.

Are these translations correct?

I suppose that would be correct Gokuyum

 Thanks Melike.

"Çekilmek" doesn´t make sense but "ayrılmak" does.

 Annem erken  ayrılmalıydı.

My mother should have left (or gone) early

My mother must have left (or gone) early

Annem erken ayrılmış olmalı. 

Thank you all for your thoughtful stimulating suggestions!

LIR correctly understood my contribution. I was referring to an assumption!