Annem erken çikimelidi (veya gitmelidi)

My mother must have left (or gone) early. Thank youuuuuuuuuu

I don´t think you can use ´meli´ here - because that means ´must´ as in ´it´s essential´ and you can´t use this in the past tense anyway. In your sentence you are ´supposing´ that she went early. I think that you should use the ´miş´ ending here:

Annem erken çıkmış

.....however, wait for confirmation (or otherwise!)

LIR thank you

 My mother should have withdrew early.

Çekilmek means to withdraw, draw back, recede.

Ayrılmak means to leave.

My mother should have left early.

 I dont think they mean that, let me try and explain

The daughter or son turns up at a party expecting to find his mother there ,he sees that she isnt there, so he assumes that she must of left early,before he arrived there.

does that make sense to you Gokuyum, maybe now you could enlighten me with your opnion of this translation

But that´s not the sentence Polyglot translated.  It was ´my mother must have left early´ meaning ´he thinks that his mother left/went out early´.  It doesn´t mean ´my mother had to/should have left early.  

It´s like saying ´I lost my wallet - I must have left it on the bus´ - this doesn´t mean I had to leave it on the bus or I should have left it on the bus - it´s means ´it seems to me that I most probably left it on the bus´

hey city, great minds and all that jazz

Edit: Got to insecure about my translation, waiting for Gokuyum with the correct answer

What do you mean?  I´m telling you what it should be in English!

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!