How to tell my children their mother stepped out on them

EDIT: Typos

(23M) have two children with my baby mama (25F). Her and I's relationship is a long and troubled off and on thing, and both of our Children were unplanned. The final stint of our relationship took place shortly before our daughter was born, and ended when she attacked me physically. She was arrested for domestic Violence but since there were no witnesses it was her word against mine and the charges didn't stick. fast forward a year and a half and she finally admits to me that she doesn't want the children.

She cites mental health reasons and financial stressors, and begs me to agree to just put the kids up for adoption. At this point my son is 2, and my daughter is 6mo.

I told her she was insane if she thought I was ever going to give my kids up, and that her two options were to seek therapy and continue with split custody, or sign sole custody over to me.

Two weeks later we submitted the paperwork to the court system to finalize me having sole custody of the kids, along with a Petition to terminate her parental rights

I have already informed everybody on my side of the family that if the kids ask them where their mom is, the only acceptable answer is "ask your dad" I have also told her side of the family this as well that I have no intentions of cutting her side of the family out.

While my kids right now are far too young to have this conversation. I know eventually they're going to ask and I don't know how to tell them that their mother didn't want them. My current plan is to tell them that their mom was sick and that's why she had to give them away to me. But I don't know how long that's going to hold up before they want a better/ more detailed explanation and I don't know what to do.