Does anyone know what I can do to bring the children's stepmother to the contact centre with me to see the children? The contact reports show how much my boys miss her and my wife really misses them and she starting to feel it now more than ever.
Have you had a look at the National Association of Child Contact Centres (NACCC) website? Or better still, sent them a message to put your situation (and question) to them?
https://naccc.org.uk/
Googling the question; "Can my new partner come into contact sessions with me?" brings up a few search results directly from their website.
https://naccc.org.uk/faq/can-my-new-partner-come-into-contact-sessions-with-me/
And their advice is that "Seeing your child at a contact centre is a very emotionally provocative event for you and your child. Initially, it is best if these sessions are used for you and your child to build and strengthen your relationships in this very unfamiliar environment" but this is not taking into consideration that this is not just your new partner or a new person to your children, it's your wife, who clearly plays a role and has an established relationship with your boys.
I may be worth a shot to find out where you stand.