I think this is both smart and reasonable.
It is absolutely true that she cannot possibly pay Kaine any money right now. How is she supposed to get a job? I know highly qualified people who have been out of work for over a year. Who would hire someone who might be arrested at any moment and who is definitely going to have other stuff interfering with work?
Whether a person is employed or not, they have the responsibility to financially care for their children. I know of some parents who won't work, thinking that gives them some justification for not paying child support. The court will still issue the child support order and she begins accruing the child support debt.
It is also absolutely true that if she were required to give a depo or take the stand in a divorce case, it could require her to either give up her 5th amendment rights OR lose her daughter. While some people would celebrate that, it isn't legally fair.
It happens all the time that civil suits are filed that are unrelated or only marginally related to criminal cases. And that sometimes info comes out. As a matter of fact, it is a known legal tactic that in a murder investigation where there may not be enough evidence for prosecution, the family may file a civil wrongful death suit against the suspect. The prosecution usually will attend the civil hearing to pick up any info that comes out in the hearing. In the Anthony case, a civil proceeding was allowed to proceed that only touched on the death of Caylee, the Nanny case. The judge may impose certain limits on certain info, but the precedence of a civil case being allowed to proceed even so.
I also think that Kaine was advised to file for divorce so quickly in order to force her to testify and this is a predictable legal response. I also think he may have blown it by asking for money. Where does he think she's going to get it?
And how can he not support himself and Baby K in the same house they've been living in with 2-3 fewer people when he was the sole supporter before? I know daycare is expensive, but he's not even back at work full time.
The issues isn't whether he needs to ask for money, or whether she can pay. The issues is that she is a parent and expected to help support the child.