Can my former employer "bad mouth" me when I write them as a previous employer on a job application

Many companies adhere to the policy of not saying anything about a former employee other than start and termination dates, but that is a matter of choice.  Adhering to that policy protects former employers from lawsuits from both former employees and those who hire them.  It's probably the smartest way to handle such a situation.  However, that doesn't mean that there is anything illegal about giving more information, if they are willing to take the risks.  The risks are that, if the information is false, the former employer could be sued for defamation (in a situation like yours, where a former employer bad mouths the former employee and costs the former employee a job or other damages) or for fraud (if it falsely praises the former employee and the new employer relies on that recommendation to hire someone incompetent or dishonest).   Thus, you may be able to sue your former employer for defamation, but you should be aware that defamation can only be faced on a false statement of fact; true statements are not defamatory, and neither are statements of opinion.