We *live* together and handle family business together. Because we're still a family. She and I don't need to be "together" for us to be a family.

Since she and I aren't together, there is no dating "other" people. it's just dating. You phrased it as, we stayed together for the kids but are free to date other people, which is not the case. That's loaded language.

Our family is still together.

She and I are not.

She and I are free to do as we please, *because* we're not together. It's not an an open relationship, which is what is implied by "staying together and dating other people.

Are you still confused?