how can i sue my ex business partner if he opened a new company that does the same services?

Your questions are too complex to really give you specifics but this is some general information. Since you have no written agreements concerning what might happen if the business broke up you may have some difficulty. Many times businesses will have members sign a non-compete agreement. Violating that agreement can be the subject of a civil case. But you do not have that in your situation. Depending on the specific facts and what the understanding was between the two of you in case your relationship ended, you may be able to assert some type of civil claims (i.e. some type of breach, fraud, tortious interference). What you might be able to claim really depends on the specific facts though. You can represent yourself but if it your company making the claim then you cannot and will need an attorney. Even if it is you suing as an individual, this situation sounds more complex and you should seek out a commercial litigation attorney. As far as him now seeking to reduce his child support, your business claims would more likely need to be dealt with in a seperate forum as the family court would probably not have jurisdiction to hear those claims. Again, discuss with a commercial litigator.