If his wife knew you and then found out that you have spent time with their children she will feel he has broken her trust and that of her children.
I don't think you have considered that the children may have a voice in this. Finding out that their Dad is with their school friends mum will feel uncomfortable. Can you see how this might feel for them? Can you empathise with them?
If he has had an amicable relationship with his wife then he should just see this as a reaction to him not being honest. They will always be parents first so he needs to find away to rebuild trust. The children are at an age where they can voice their feelings. He needs to genuinely listen and not assume his wife is behind any objections they raise.
Those who say Dads are alienated and courts don't support Dads are not giving a balanced view. Courts take it very seriously and in some cases to the detriment of children. I.e children being forced to spend time with aggressive Dads despite telling Cafcass how scared they feel.
You are fortunate at their ages the children can speak for themselves. They might not want you on the scene with them for a while, which I think you may just need to accept. They don't need a relationship with you.
Your bf needs to start the divorce, keep dialogue with his children open and see you separately and not involve the children.
Take it really slow and in a few years it will be settled..you might not want to wait but as parents the priority has to be the children.
PS make your bf get his own place, don't offer him your house as you are an easy option and he could just go from wife to his mums then to you. Make him stand on his own two feet first