There is no difference. But, the second sentence using "for" is better and as Bill stated, it "for" gives better emphasis.

We provide help [to] families in crisis situations - sounds more like an explanation or definition of sorts as to what the services are. We provide help [for] families in crisis situations - sounds more dire, you'd usually hear this type of statements from people responding to natural disasters. The emphasis is more on the function of providing help right now, as opposed to in general.

The first sentence the emphasis is on families they are who you are helping. The second sentence the emphasis is on providing help. Who do you help? We provide help to families. Sorry I forgot, what do you do for families? We provide help for families. Hope you understand the difference now.