Its just important to make sure they know no matter what happens they will be taken care of and you will be there for them. When they see one parent leaving the other it can put the fear in them that they are going to be left also. So focus on making sure they know they will be ok and provided for.
My kids had a rough night also. W dropped off both of them at my apartment and D4 began to cry when she was trying to leave. W stayed for 5 more minutes holding D4 in her room before she left and I could tell it was bothering W also. When she left I tried to comfort her but she just kept saying "I miss mommy" while crying. Stay strong for those little ones everyone. Its difficult for them to believe everything is going to be ok when they see us break down also, so do your best to be that pillar of strength they need right now.
Accept what is, let go of what was, and have faith in what will be