Hi Annabelle,

There's a very short example of the three umlauted vowels in German (ä, ö and ü)
here

One way it's sometimes described is that you purse you lips as if saying "oo", and with your lips in that position try to say "ee" instead!

The sound is certainly not "ee" except in some dialects such as Berlin - interestingly, in the German version of "My Fair Lady", the equivalent of "The rain in Spain stays mainly on the plain", the sentence which Higgins uses to get rid of Eliza's "RIne in Spine..." pronunciation, is "Es grünt so grün wenn Spaniens Blüten blüh'n" - literally "it blossoms so greenly when Spain's blossoms bloom". Eliza's Berlin pronunciation which he wants to eradicate is "es greent so green wenn Spaniens Bleeten bleehn" - very much like your Grandmother's pronunciation!

Here are Stefanie Schaefer and Christian Grygas at the "by Jove she's got it!" moment, and you get a good view of how Stefanie is forming the vowel!

here