There is a lot of information on the website and that information can be very confusing.
Prior to mailing in your petition, I would strongly urge you to check all of the requirements on the embassy website. Otherwise, your application could be rejected. DCF filing is for people who have established permanent residency in the UK. And based on what I've read in previous posts of people who have filed recently, the way that I understand it is that you have to have resided in the UK for two years or more.
Immigration falls under Dept of Homeland Security, and as such, I would be to play it safe and by the rules. It would be a shame if you submitted everything, only to be turned down because your residency timescales don't meet their requirements. This is particularly so because I'm sure you don't want to waste time when you're keen to get back to the US for your mom.
I can say that during my entire petition and process, everybody in immigration that I dealt with, either on the phone, by email or at the embassy the day of the interview, was very nice, pleasant and helpful. They aren't there to go out of their way to make things difficult on purpose. They are there to make sure the rules and procedures are followed. It's the rules and procedures that can be frustrating at times, and believe me, I had many, MANY a sleepless night over it.
Again, good luck and if you pm me with any questions, I'll do my best to help you, based on what I know from our case.