is there a minhag for the father of the kallah ( as well as the father in law) to bless the kallah at the badekin with the standard yesimeich elokeim bracha+ the long nusach of that brocho that is in the yom kipper machzor that we say erev yom kippur. what is the makor for this nusach?

ב"ה Shalom The earliest source I found is in one of the Rishonim , in the Tanya Rabbati chapter 91. However, it is not specified what is the nusach of the bracha and who gives it. However, in the kitzur Shulchan Aruch 147:3, he writes that the minhag is that the elders of the city say " אחותינו את היי לאלפי רבבה" from Bereahit 24:60. I personally have not seen this done at a wedding, rather I have seen the parents and grandparents give the bracha. However, the fact that I have not found other written sources, does not mean there are not different minhagim. In my family,for example, the minhag is to say as we say on Erev Shabbat or on Erev Yom Kippur כשרה רבקה רחל ולאה ישימך אלוקים without the long Nusach.You should ask other people in your family what they remember as the family minhag. All the Best