When my parents separated my brother had terrible nightmare for months. He would wake up sobbing and afraid that my mum was going to leave him. My parents however did get back together and so that helped somewhat after that.
I have found that even if there is nothing stressful going on children need bedtime to be a refuge for them. Its a pleasant time together with their parent that no matter what has gone on during the day. Bedtime routines should make everything feel better again.
Your children may need extra stories, snuggles and songs to feel secure because children cannot sleep when they are anxious.
Finding ways to minimize stress during the day will also help. Make sure they see as little of the adult stress (mainly anger, harsh words etc) as possible and they will find comfort in their new routine. This doesn't mean extra treats or no discipline but it means more snuggles, more playing with mummy, more of your time if you can.
I was told by therapist that even 10 minutes of extra one on one play with a child everyday can make the difference in transitions. The kind of play you need to do though is child led play. This is where the child controls everything that happens in just those few minutes and you just go ahead and play too with them deciding what happens. You have to do one son at a time though. It has really helped my oldest son when my husband wasn't around because of work and school. I know the situation is different but he was acting out violently and it was terrible.
Good luck