You should contact an attorney experienced in Fair Debt Collection Practices law. It is possible that this law firm is violating the law. Many law firms, including mine, offer a free initial consultation so you have nothing to lose.
The lawyer who is contacting you is correct. Your mother, by co-signing, agreed that she is responsible for repaying the loan in the event of your default. If you defaulted, then she is at risk of being sued. And if the plaintiff prevails, they will have a lien on your mother's house because a civil judgment operates as a lien on real property. Bear in mind that if you are considering defending a lawsuit, any communications you exchange with the plaintiff's attorney in which you admit to the debt may be offered as evidence against you in court. As to settlement, $5,200 is no great deal on a $6,000 debt. You should not even seriously consider any offer over $4,000. If you are ultimately sued, you should not try to handle the matter pro se. You should retain an attorney experienced in debt-collection defense to represent you.