How often do your dc have contact with their df and do they stay overnight/spend holidays with him? Are they eager to see him and do they appear happy/sad/indifferent when they return home to you? In what way is your 11yo ds "really suffering"?
At 8yo he emerged from the years of 'magical thinking' to a reality in which all he'd known was altered and it's possible that, in his perception, this change appeared to take place overnight giving him little time to fully comprehend the new order and the reasons for it.
Could he be holding himself responsible for his dps splitting up? Does he feel he has to be the 'the man' of your household? Do the majority of his friends live in happy 2-parent households?
Both of your dcs may be conflicted because the life they lived with you and their df was all they knew; it was their 'normal' and they may still not appreciate the extent to which it was, in fact, abnormal.
As you''ve been separated for more than 2 years and your h is moving in with his gf, now could be the optimum time to petition for divorce by mutual consent which will provide opportunity for you to have age-appropriate conversations with each, and both, of your dc as to why it was not in anyone's best interests for their dps to remain living together as a family unit.
Your live-out partner sounds about as much use as a chocolate teapot is clearly a less than impressive role model for your boys and, depending on how much contact they have with him, this may be compounding any feelings of conflict they are experiencing.
To their minds replacing their df with another misery guts who cannot relate to children may seem inexplicable behaviour on your part, but neither of them are yet at an age where they can easily verbalise complex feelings.
Your eldest is now on the cusp of puberty and my concern is that he may begin to mirror his df's behaviour towards you, with the inherent danger that your youngest may follow in his older brother's footsteps, so to speak.
If you're feeling that history is to some extent repeating itself in your choice of men to mate with, counsellng may help to unravel why you settle for less than you deserve but, imo, your priority should be to arrange some form of therapeutic input for your dcs before their teenage years bite you on the bum as, needless to say, they're unlikely to express or act out any hormonal angst to their repressive df.
Another carrier bag/bin liner fan here - life is far too short to hose out smelly bins 