Someone somewhere said that instead of crying, Minerva should have apologized to everyone. Well my response, first of all she just got back, give her some space, but really the only person in ST is wronged was Sting for pretty much taking Lector hostage, and they probably resolved that on their way back off screen. Everything else that is all on Gemma, she might have been second in command, but still as we saw in her flashback she is also a victim of his crap. I guess she could have said "I am sorry my father is such a duchbag." If she said on behalf of her father she is sorry, that would be a lie, because Gemma is not sorry, in fact he is an even bigger duchbag than he was before. Though it would be nice for her and Yukino could talk about stuff Gemma did to them.
If she should apology to anyone, first of Lucy, but Erza can pass that message besides Lucy has her problems to deal with and she is not one to hold a grudge. But after that, she ought to Mermaid Heel and apology to Kagura and Milliana for what she did to them, perhaps if she went with Erza they might hear her out. I think Kagura thinking would be if big sister Erza forgives you, than I can forgive.