Like others have said, right now you need to appear stable, normal and in control around your kids. Stay positive. Kids are smart and they are also resilient. Having Mom take off is going to cause confusion, so do everything you can to maintain normalcy for their benefit.
Don't involve them and for right now try to shelter them from any chaos or uncertainty.
If you have a church home, then seek guidance and counseling for yourself right now. Most established churches will have experienced staff members who are responsible just for these types of life incidents and getting sound, experienced counseling is going to help you a lot more than trying to tackle this as a team of one.
Stay positive...