You are in the wrong on many fronts. Including that information in the OP is a good idea so the bigger picture is understood.
Your friend has very clear romantic interest in you and likely has for a while, she doesn't respect your relationship with your girlfriend, and she doesn't want to give up trying to steal you from your girlfriend. Until she can respect your relationship, you should not be alone with her. Even if you didn't consider going to the beach with her a date, she was trying to take you on a date. By trying to be her friend, you are probably leading her on and she probably thinks the attention you are giving her is an indication that you have romantic interest in her that is held back by your current relationship. She probably thinks that being persistent and pushing or overstepping the platonic line will be rewarded. If you have no interest in her, she needs to know that.
Your girlfriend's issues related to being cheated on need to be considered. She should be working on that, but you need to work with her on that by being open and honest to build trust because she doesn't trust you. If she doesn't know the whole story between you and your friend, you need to tell your girlfriend everything. Understand that your girlfriend probably is paranoid that you are going to cheat on her like that other guy and she may constantly be looking for signs that you are or will cheat on her because she probably looked at the last relationship for signs that she missed and is applying that to your relationship. If the two of you don't work on her infidelity concerns, it will drive a wedge between the two of you and lead to the relationship failing even if everything else in the relationship is fantastic. It isn't fair to you for her to suspect you might cheat on her just because some other guy did, but your history with your friend has given your girlfriend plenty of cause to be suspicious of you.
You also should be thinking about what is best for you. There are two women that want to be with you and one might be better than the other, even if that isn't your girlfriend. Staying with the wrong person isn't fair to 3 people.