I think that the second part ***explains the first***:

> **We can't run this bar without her.** [Of course we can. I meant we can]
> **Not** [do *both* run this bar without her] **and raise two kids.**

<sub>(Other answers have explained ***how*** the first part is inserted into the second part. But I think it's important to explain what the outcome is, the ***why***. That, as said, the second explains the first.)</sub>