"deine Freundin" is the subject, then it goes soon after the verb.
Maybe you make confusion with the rule that says that Dativ goes before Akkusativ and anyway if there is a short pronoun it goes before.
Ich habe Dir meine Freundin vorgestellen...
(I am no native German... but I hope I got the meaning of your question...) ;)
My grammar sheet says there's no ending for the possessive adjectives in the nominative (giving "Mein Garten, Mein Jacke, Mein Haus" as examples). In the accusative, however, feminine nouns take an -e. But Freundin isn't in the accusative here, is it? Or is my sheet wrong?
I had them also confused, a long time ago. But "Freunden" is not the plural of "Freund", the plural is "Freunde". In dative case, however, "Freunde" does change to "Freunden". So I'm guessing you can tell which is which by the word and the article:
"Meine Freundin" - article ends with "-e", name ends with "-in"
"Meine Freunde" - article ends with "-e", name ends with "-e"
"Meiner Freundin" - article ends with "-er", name ends with "-in"
"Meinen Freunden" - article ends with "-en", name ends with "-en"