´Yalnız benim emrimde çalışsınlar ve yalnız bana kumaş dokusunlar."

Im not sure if Ive come across this yet in my studies so far. I have no idea when to do this so the only example i have is from a sentence in the story Im practicing translating. (and its from the website Abla showed me 

Is there anything to know on this so I can know when to use 3rd person plural (-ler) with 2nd person singular (-sin) tense? Or is there another way I should think of how those verbs are being used in that sentence?

Turkish suffixes are not always easy to distinguish from one another..

gel-i-yor-sun, gel-ir-sin, gel-ecek-sin, gel-miş-sin,.. 

As you may notice in the examples above, 2nd person personal ending (-sin,-sın, -sun, -sün) always follows a suffix when added to a verb.

If it is directly added to a verb stem, it is no more for 2nd person, but for 3rd person imperative:

gel-sin

And its plural is:

gel-sin-ler 

...

çalış-sın(lar), gül-sün(ler), doku-sun(lar)

wait for objections

As a learner like you, Mavili, I understand what confuses you. It shows in this table which I once made in order to explain the personal endings to myself. The same information can be found everywhere but I think it is good to see them once side by side.

Your problem is marked with blue:

Four sets of personal endings:

The present tense personal suffix of sg 2^nd is the same as the imperative personal suffix of sg 3^rd (and pl 3^rd respectively). To distinguish these forms from each other when you meet them in real life, read carefully what scalpel wrote.

Notice that in the table only the front vowel variants of personal endings are represented. You change them according to any vowel harmony rules you know. The table is probably oversimplified (and no one has checked it  -  yet) but it has helped me. Maybe it can help you, too.

Ah! şimdi anladim I would not have thought of Imperative mood. And I had not studied that mood in depth yet. But I really do understand so its just a matter of learning to recognize it when I see it. Thank you Scalpel and Abla. I´ll definitly have to use that chart for reference. I couldn´t figure out that its not double pronouns, its actullly written verb + -sinler/sunlar/sınlar/sünler, correct?

oynasınlar -Let them play

So for my sentence, Im still not sure of the context that the first yalnız is being used, or (emrimde) so there is still some gaps.

yalnız benim emrimde çalışsınlar ve yalnız bana kumaş dokusunlar. -on my remedy alone, let them work (and let them) only weave cloths for me.

Yes, mavili, "its not double pronouns, its actually written verb+-sinler/sunlar/sınlar/sünler"

Your sentence is made up of two independent sentences:

Yalnız benim emrimde çalışsınlar (yalnız benim emrimde= only under my authority/order)

Yalnız bana kumaş dokusunlar (yalnız bana= only for/to me)