The housing authority is a good place to seek council and advice. In most cases a land lord will and can give a 30 day notice without giving any reason and this is how notice is most often given. Lack of paying rent does not take a 30 day notice. Your perfect history and being a single parent has nothing to do with your eviction. If you were given the notice to vacate that stated that you were being removed for complaining about unsafe living conditions then you probably have a pretty easy case. If it states that it is for clean up then it may not be so easy if there is a case at all and if there is no reason at all given (the most common) then it would likely be a very difficult case. You should seek competent legal advice and there are many sources for you to do that with low or no cost to you. You might even talk to the local HUD representative.
I hope this helps and that you are able to get things settled in a beneficial way for you.
The scenario described just doesn't sound right. If you have a written lease check it for the provisions that tell you how your lease can be terminated. We are not lawyers, however, and cannot give you any legal advice. It may be best to see if you can get a consultation with a legal counsel.
Also, check your county website for landlord-tenant affairs and see if you can get help through the local Housing authority, non-profit groups etc.
Good luck & best wishes.