I am in the same boat as a single mother to a 10 year old, I have been honest with her in terms she can understand and have used days like "R U Ok' day to open up a conversation with her about what mental illness is.

I hope I am successful in bringing her up with enough compassion and understanding to fully understand and accept what mental illness is....Also I feel it is very important let her know that it is ok to feel whatever emotions she might feel in regards to my illness and to be honest about that too

It is tough. I think being open and honest is the only way through it and acknowledge that the stigmas that are wrapped around having a mental illness are as pointless and archaic as racism/sexism etc