My advice is don't go through with a threesome if your partner isn't comfortable. She is the one who asked in the first place, but she has shown you that she is jealous and now is pushing blame for her actions to you when you were just doing what she asked. She is not in a comfortable place in your relationship to be adding more people into the mix. I suggest she work out her feelings and don't try adding anyone else or polyamory unless you two can communicate fully in a safe and healthy manner. Also her behavior is kind of red flaggy to me personally, so just watch it.

She should try to look at herself and why she is upset. Why did she want the threesome in the first place? Why wouldn't she join in? And why did she get mad at you for just doing what she asked? If she can address these questions within herself you can maybe start a conversation on how to move past this and approach things in a different way in the future.