Translation:The mother of Monica is young.
Why does "of Ana" become "Anei", but "of Monica" becomes "Monicăi"? Is this because "-cei" would significantly alter the sound of the name itself?
I am not sure what the actual rule is, but yes, it just sounds wrong. It's the same with 'Anca' -> 'Ancăi'. Also, names ending with a consonant and newer names of foreign origin use the masculine article.
It's effective a rule that you need to understand it.In Romanian Ana becomes Anei Monica-Monicai,Mariana-Marianei and others.
And "Olgăi" came to mind too, so it must be to avoid the "ce" and "ge" sounds. I forgot what they were called, but they were similar to "ci," "gi," "che," "ghe," "chi," and "ghi."
I provided more details on that rule here:
so is the nominative case Monica or Monică?
Nominative is Monica.