FWIW I helped a friend go through the paperwork process for food stamps in Texas (actually a debit card - who knew???) within the last 18 mos. Her husband emptied the bank account and moved out of the house leaving a SAHM w 3 kids, a huge mortgage, and no money. For food stamps there was no requirement that the father be contacted at all. She was very worried about that because she thought he might fight her for the kids and didn't want him to know that she was receiving aid. I don't know what would have happened had she applied for more than food stamps. He kept the kids on the insurance so she didn't apply for that.
The town that her parents live in/near has just over 1000 people "in town". There is a good chance that they live outside of town where "sewage" would be "septic". Probably at the time that the trailer was put in, if it needed a separate septic system it would have only cost a few thousand dollars. Current laws often require a more complicated version of septic system and it would have been more expensive. There is also a chance that they hooked the trailer up to the septic system that was already in place for the parent's house. I have the older style septic and it is oversized for the house as it was put in with an addition/pool house build in mind. To hook up to that would have been a minimal cost.
As to the water, again assuming that they are outside of the city limits, there are plenty of cases around here where all of the water supply on a particular property comes from one water meter. I have family in the general area that run 4 different buildings from 1 meter. It is all legal in their case, barn, work shop, well house has a bathroom (well is to fill tank/water stock when water table is up), house. Of course, the family could be running purely off of well water - not too common here, but not unheard of either.
Also, remember a "yard" might well be a number of acres. I live in a subdivision outside of town and my "yard" is measured in acres.