One way to give them more money and not incentivize single parenthood (which is the issue, not divorce, and treating them as equivalent has always been wrong and is increasingly so as marriage rates drops) is to go to UBI instead of means-tested aid, or, if using means testing, use a means-testing formula which doesn't punish two-parent families.
> Children being raised by single mothers is not a good outcome.
Its a lot better than children being raised by two parents together, one of which is abusing them and/or the other parent, which any change which does more to avoid incentivizing divorce or single-parenthood more than eliminating any two-parent penalty would incentivize, especially for the poor.