🚀 go-pugleaf

Is this more along the lines of what you want?
1. Get ready to place text at the end of myTextFrame
--- This code is simplifying things it only works if the text to add will be the last item in the frame, I don't know how to indicate that it should go after Paragraph 1 unless something like this (Set MyInsertionpoint = myTextFrame.Paragraphs.Item(2)) works. So you want to set your insertion point to the last item in the frame the item(-1) :
Set MyInsertionpoint = myTextFrame.InsertionPoints.Item(-1)

2. But before you place it you need to set that the new text has a style, in this case I use a paragraph style named "Italics_Style", so you set the style of the insertion point (undoubtedly you could change this to character style:
myinsertionpoint.ApplyStyle myDocument.ParaStyles.Item("Italics_Style")

3. then place the text:
myinsertionpoint.TextContents = "Your String"

Final code:
Set MyInsertionpoint = myTextFrame.InsertionPoints.Item(-1)
myinsertionpoint.ApplyStyle myDocument.ParaStyles.Item("Italics_Style")
myinsertionpoint.TextContents = "Your String"

(There are some long discussions about how to search for specific text in the Archive that might help if the location of the text to place moves around)