Learn Turkish: Yengem gelene kadar yeğenimle kalmam lazımdı. - I had to stay with my nephew until my aunt-in-law came.

This uses the structure for past necessity. First, we turn the verb kalmak (to stay) into a short noun using -ma, and add the possessive -m (my) to make kalmam (my staying). Then, we add lazımdı, which is lazım (necessary) plus the past tense suffix -dı. Literally, it translates to 'my staying was necessary'.

How do we get 'until my aunt-in-law came' from gelene kadar?

To say 'until someone does something' in Turkish, you add the suffix -(y)Ana or -(y)ene to the verb root, followed by the word kadar. Here, gel (come) becomes gelene kadar (until coming). Notice that Turkish doesn't mark the past tense on this verb; the past tense in lazımdı at the end of the sentence is enough to show the whole event happened in the past.

I learned that 'aunt' is teyze or hala. What is a yenge?

Turkish has very specific words for relatives. Teyze is your mother's sister, and hala is your father's sister. Yenge refers to a female relative by marriage, like your uncle's wife (aunt-in-law) or your brother's wife (sister-in-law).

Why is it yeğenimle instead of using the separate word ile for 'with'?