Yes, younger kids do get suspended but it seems to be more prevalent in some school systems than in others, and in some specific schools than in others. In our area, certain Washington, DC charter schools have had issues with relatively high numbers of suspensions of young students, and that use of suspensions is being looked at hard, to see if it's appropriate, overused, etc. A lot of the coverage has focused on how suspension should be, and usually is, an absolute last resort.
This is really not about whether the school in your relative's case is overusing suspension -- it's more about whether the girl has some issues that are serious but mom does nothing at home to reinforce school discipline.
In your relative's child's case, rest assured there is FAR more to the story than the mother is discussing -- and probably far more going on with her child at school than the mother herself even knows. It sounds as if the girl has serious behavioral issues, or other issues that may be unidentified or even undiagnosed (sounds like there might be certain conditions going on there like oppositional defiance disorder?). When you say the girl seems to lack any remorse -- that could be a sign that there may be a psychological issue, probably made worse if mom is as you say a poor role model....
If anyone in the family is closer to this mom than you are, maybe someone would be open to starting to take this poor girl places at times, attend her school functions just as an interested aunt or adult cousin, or whatever. The girl is probably crying out for help by acting out badly. If her mom can be convinced to see the school counselor and classroom teacher together for a conference it would help; would mom listen to anyone in the family about doing so? Or would mom just get defensive and angry and say that her daughter has zero responsibility and is just being "labeled"? I worry for this girl if mom is just blaming the school and not seeing that the girl needs help right now.