The lawyers appointed by the insurer represent the defendant and, indirectly, the insurer.
"Bad Faith", on their part, would be actions contrary to their clients interests, NOT contrary to your interests. If, for example, they were holding out for a trial instead of a settlement because they would get paid a higher fee, that would be bad faith. Declining to settle in hopes of pressuring you into accepting a lower offer is what they are paid to do.
In most cases, insurers authorize their lawyers to negotiate on their behalf. It would be up to the lawyer to decide when, and whether, to settle or go to trial.
You can try googling CPS plus the name of your state to get your CPS website. It should tell you the definitions for abuse and neglect in your state. There also may be a place to complain about treatment.
Here is a website that may help with some aspects of the legal problems: http://www.fightcps.com