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...