Glad that's helped Cheated On - what I'm saying applies to both you and the OP. You cannot control another's behaviour choices - whether it's infidelity or any other major flaw. Only the person concerned can control that, just as you're the only person who can control your choices. When someone makes monumentally bad behaviour choices, it is their responsibility to get to the root of it and make changes. You can however choose to insist that they do that before you resume or re-commit to a relationship with them.
If they fail to do this - or you choose to carry on without them having done this work, there is every chance the same behaviour will happen again.
Rosyred, you are not responsible for the behaviour choices of the people in your life. There is nothing about you that makes people lie to you - it is about them. There's nothing your brother did to deserve the blow that was dealt him - he was not responsible for his wife's affair.
Assuming your H is thinking of using a private psychotherapist, there should be no delay whatsoever - so I'm not sure what you mean by "starting the proceedings" to see one. Yes, it is common for cheaters not to want discussions about their behaviour, but my God it's necessary that they do discuss it - if you need to - otherwise they will be forever in denial about their actions and you will never start to heal.
I am frustrated at your doctor's panacea of Relate - this will not be helpful just yet. Your H needs to start work on himself first.
What I really do think would help you is your own counselling space - I think you need bereavement counselling and separate help to process the awful events you have faced. When too many bad things happen to us, it causes us to lose our faith with the world and our ability to cope. In the absence of ADs, you need help and care to get you through this.
Glad you texted the SIL - that is now dealt with and you should focus on you, your family and your own relationship.