What is the consensus of continuing a friendship after it has been disclosed that you have cheated on your SO with that person?

My SO has a friend who he had a physical relationship with but is no longer doing so. He has continued this friendship as he sees her when he takes his children to school and they may have a coffee together at the local McDonalds.

He confessed that 4 months into our relationship he had sex with her and it was a one off mistake. I have been with my SO for 9 months. I decided to try and forgive him and move on as I understood where he was in his head when he cheated on me. However, having seen text messages and from what my SO has informed me he knows he could go there again with her and she has practically admitted that he has it on a plate if he wants it.

I’ve agreed to meet half way with my SO and asked him that if he is choosing to continue with this friendship that they meet in public places and he has agreed.

My SO has now informed me that she is due to move into a new house and would like him to sort her gadgets out. I’ve told him that I don’t feel that it is appropriate for him to go to her house given that I know she would ‘have him’ at any given opportunity, although he reassures me that he will not have sex with her again.

I have stated to my SO that if he chooses to sort her gadgets out then he has to end it with me as I will not agree to it. My SO has said that he finds my attitude very bizarre.

Am I being too harsh…bunny boiler material maybe? What is the general consensus?