Cjbrady, having it said that you were dishonorably discharged when, in fact, you weren't, could be considered by a court to be defamation per se and, with defamatory per se statements, reputational injury is presumed and damages can be awarded on this presumed injury alone. You do not need to show any economic losses resulted from the statements made (no loss of job, no loss of income, no monetary damages of any sort).
However, damages awarded on presumed reputational injuries alone are often not enough to warrant, or to cover, the high costs of pursuing a defamation action. The costs of a suit can be especially high when the defamatory statements appear online and originate from a different state.
I agree with antrc170 that the first best step to take, if your ex sister-in-law will not remove the postings voluntarily, is to contact Facebook and file a complaint. The site may remove the offending material on your request and without a court order, especially if the material posted violates Facebook's terms of service.
The next step, if this does not resolve the issue, is to contact an attorney. Just a cease and desist letter issued to your ex sister-in-law from the attorney, threatening legal action if she does not comply with your requests to remove the material, may alarm her enough to remove the postings from her Facebook page and stop her from making any additional derogatory or defamatory comments about you.
A lawsuit, because of the costs involved and the "iffiness" of a win in any action, should be the very last option you consider - and this only after a consultation with an attorney who can best advise you on the merits of a suit, and the pros and cons of filing, after the attorney has had a chance to review the material posted and review all of the facts.
Being called "trash" or a "baby," by the way, would not be defamation, cj - these are opinions and opinions are protected by the First Amendment although, as Charlotte implied, the "baby" term seems to be a fairly accurate description of you, based on your reaction to the advice you have received here. "Taking the law into your own hands" is never a good idea and it would be a very childish thing to do and, legally, it could be a dangerous thing for you to do.