import re

regex = r"\d{2}\/\d{2}\/\d{2}(?:(?!\d{2}\/\d{2}\/\d{2}).)*string(?:(?!string|\d{2}\/\d{2}\/\d{2}).)*\d{2}\/\d{2}\/\d{2}"

test_str = """01/20/20\n\n"
	"string\n\n"
	"01/21/20\n\n"
	"01/20/20\n\n"
	"this isn't the phrase you're looking for\n\n"
	"01/21/20\n\n"
	"string"""
	
print(re.findall(regex, test_str, re.DOTALL))