I think 'ihren' means 'her', not their. (''i'' wasn't capitalized.)

evlilik yıldönümlerini => evlilik yıl dönümünü

(also yıldönümü => yıldönümü)

If I'm not mistaken (correct me if I'm wrong), "ihren" could be construed either as "her" or "their". It's up to us to understand it either way, according to the context.

What you suggested, "Ihren" (capitalized), could refer not to "their", but to "your" - as a form of respect.

Again, if I'm wrong - I'll stand corrected.

Sentence [#1759822] makes me think this sentence.
I sent a PM to brauchinet one hour ago.

By the way, I tend to agree with you that "ihren" here meant "her" rather than "their". I simply made my above comment in relation to "Ihren" (capitalization could only indicate "your" rather than "her" or "their").

So this is funny, 'ihren' here can mean both 'her' and 'their' (his and her's together as a couple) and the meaning wouldn't change in German. So I'd say German and English match.
Of course, 'ihren' could also mean some other couple's anniversary, but one would need a context for this interpretation.
If you'd capitalize 'Ihren', that would mean 'your anniversary' as 'Höflichkeitsform' and that would be different from both English and Turkish

So it depends on how you would say in Turkish. If she forgets 'her' own anniversary, she ayni zamanda forgets 'their' anniversary.

Thank you, brauchinet. Your explanation is pretty useful for me.

I added the English translation.

In the light of a new morning my explanation is pretty confusing...Sorry for making this all too complicated.

We need a conclusion, what maku is supposed to do with the sentence.
I see you have already added a sentence where 'yil dönumünü' is singular.
Can it stay in the plural form here? Would that mean 'their first anniversaries' (of different couples)? I guess that is too improbable for a useful sentence and not within the meaning of 'their first anniversary'.

First of all, we can say ''their anniversary''. No need to make it plural, I think. http://www.ldoceonline.com/dictionary/anniversary

Turkish sentence both mean her and her husband's anniversary, and a different couple's anniversary.

But this one may mean a different couple's anniversary. Because I'd say: ''She forgot their own first wedding anniversary.'' Kendi evlilik yıl dönümlerini unuttu.