Wow what a difficult situation for you all. All I can suggest is that when they are around you let them know that they are loved and wanted, I have been in their shoes and I know that the last thing I wanted was for my parents to put each other down in front of me, They need to know that they are free to love you all without feeling bad. With the toilet training, that is something that can take time, and with the mother not helping it must be very confusing for the child, kids will still have accidents every now and then, the best thing is to praise for her good efforts and make as little a fuss as possible about the mistakes, sometimes toilet training can be hindered by anxiety.
I suppose you have talked about doing the best for the children with the mother and asked her to act like an adult and keep the children's best interests in mind, if not she sounds like she needs a reminder as it sounds like some very childish/ selfish behavior on her part.
Good luck, and give those kids the love they need