A few things from a social worker's perspective:
1. In most states, it is mandated that homes with children present MUST HAVE running water. Electricity and gas are considered optional, but if a child is to remain in the home, it must have running water.
2. I would not turn them into child protective services, as being shitty with finances and not having utilities constantly running is not enough to warrant their time to investigate. They have bigger fish to fry. My guess is that if the water is turned off, they have it turned back on in a day? CPS would consider this kind of report very low priority, and chances are that it would not be investigated for several weeks, if ever. CPS only responds same day of the report if a child is believed to be in imminent danger of death.
Also, if your sister in law is a nurse practitioner, even having it noted that she has been investigated could harm her career. It isn't worth it, unless you're truly worried about neglect or abuse.
What I would do is let them know about your state's requirements for utilities when there are children in a home.
3. One of the key tenants of social work is "never work harder for your client than they are for themselves". There are many reasons for this, but the main one is to create change, people have to be personally invested. If you do all of the work for them (paying bills, filling out all applications, etc.), they don't have to invest anything of themselves, and chances are very small that they will make a permanent change.
Hearing their professions, it is very unlikely that they'll qualify for state services. I think that your best bet would be to tell your brother that you're really worried about them, and that you're extra worried now because you aren't in a position to help them financially any more. I'd tell him that you're considering getting them time with a financial planner for Christmas, and see how he responds. If he seems interested, go for it. If he seems irritated or ambivalent, don't waste the money.
You sound like a wonderful person.