Hi Influx, welcome to SR!
I'm chiming in with another vote for the truth as much as possible, in the most age-appropriate way. My daughter is 8 & I am constantly amazed at how capable she is of handling the truth... and the most important part is that it helps her faith & trust in me to stay strong because she knows I won't lie to her.
We often sit down & discuss AH's sobriety & recovery as a family, out in the open so that everyone is present & we cut miscommunications down to a minimum. That way AH is able to hear her thoughts & concerns 1st-hand & not through me. Based on the ages of your children, I'd suggest something similar. Good luck!