Smiley, seriously, look at your relationship even without these revelations.
He is selfish in the bedroom
He is controlling
He turns arguments around so that the focus is on you and not him.
Are you really happy with this man? Does he treat you with respect and cater for your needs?
I don't know if he has changed. Why leave the profiles up if he has? Why not delete them unless he thought he might use them at some stage?
Have you looked on other dating websites?
Thing is, you now have this seed of doubt in your mind. Can you honestly trust him? Do you know that he's alone whilst away?
How would he react if you told him you couldn't have sex for a while? Would be be caring towards you, worried about you, respectful of your decision? Or would he sulk and pressure you to give in?
Only you know what kind of relationship you have with him. All I can tell you is that you should never settle for second best. You deserve more. Don't just stick with him because it's the safest option unless you want to throw away your chance to be happy. Happiness is not something that should be compromised on.
I would want to know why he has not deleted the profiles.
Why he set them up.
What he is going to do about it and how he can prove himself to you.
Actions speak louder than words. Sending texts every day is easy and it's a great way to keep you focused on him.
I'm not saying you should walk away but I do think you need to consider what role you both play in this relationship and if that role is equal. If it isn't then you do need to act because I have a feeling that sooner or later, he will reactivate one of those profiles and seek his fun elsewhere. The intention was there - what has changed since?