As far as WIC, A friend of mine has worked there for several years and she basically described it as income based. so if you put the father's name down, they are going to attempt to find income from him, which can include child support. Thus, that could lower your bottom line assistance.
However, this is what my friend counsels every person that comes in...DO NOT attempt to use this as a supplement to income. If you miss appts, etc. you can be "disqualified" and removed from the program. any assistance you should receive is a bonus to what you are already providing.
That may sound harsh, but they see people EVERY day that attempt to work the system and they don't have a very high tolerance for that. Your circumstances may have arrived due to an unfortunate accident and they are compassionate about that, but they EXPECT someone applying to show proof of either gainful employment or that they are seriously attempting to provide a competent healthy lifestyle for the family.
Not sure if that answers your questions. Here is a website:
http://www.fns.usda.gov/wic/