Dear WR, it is H who is trying to gaslight you and make you out to be the 'bad guy' in this process. He's projecting his inner turmoil and guilt on to you so he doesn't have to look at himself. Just typical MLC blather.
I am sorry that this is happening to you right now. You're a great Mom!! Continue to stay true to yourself as a person and as a Mom to your boys.
Are there any steps you can take to ensure that your communications with your L are private and confidential? What can you do to ensure that the boys are away/not around when you do talk with the L? This is within your power to do so.