Why is this girl being weird with me?

this is gonna be long!! well, I had been best friends with this girl for like 3 years and about a year ago I started to get really annoyed with her for a few reasons...she was bossy, she was ALWAYS right ( she rarely was but she wouldn't admit that she was wrong), she was so possessive and wouldn't let me have any other friends so I basically just walked away from her and found new friends. I have now been best friends with this other girl for a year and she is funny and nice and I really like her. But I also thought that maybe I should try and be friends with the first girl again since even though she had bad qualities she could also be very nice and fun so I wrote her this letter to apologise for what I did and after that our friendship started up again an I had both girls as my friends. But I knew that both of my friends would never like eachother as they always saw the other girl as competition. Now suddenly randomly after being so nice to me before my original friend( the bossy one) has gone all stiff and possessive with me again, the strangest thing is that when I am with her alone she is really nice and kind but when I am with other people and her she is so horrible. Here are a few examples of her being weird with me....we made this hat together and we had to parade it at 2 oclock (this lady told us) but at 10 to 2 oclock this girl was like we have to go and do the hat now and i was like we still have 10 mins so lets go and do something until 2 oclock but she just wouldn't admit that there was 10 mins left and that she was wrong, in the end i just walked off by myself. Also her and I both wanted to buy this thing from this shop and I didn't want to go alone to buy it so i said to her, lets go together but she is just like no you go, i dont want to and then this other girl comes up and asks the same question to this girl and she is like yeah of course ill come with you! Also when I am with my other friend she always pals up with someone and links arms with them and its like she wants to show me that they are best friends and rub it in! Sorry this was soooo long, thanks for reading it!!