How sad for these beautiful kids and their families. I always say you need to keep an eye on young children ALL the time, you never know what they're up to. My thoughts and prayers for this families at this very difficult time.
Typically, there will be nothing done and it will be declared an accidental death. The parent that backed over the child got all the sentence they will ever need as they will have to deal with the responsibility/guilt of killing their child and the unstated/maybe stated blame of their spouse. I don't believe that the percentages for husband and wife staying together after something like this is very high.
Terrible! I believe Vincenzo is right about the breaking up part specially if your spouse is the type to keep a grudge then this will come up every time there is hurt feelings.