This is the same child who was 6 in October, right? So she just had a birthday. Here's your question from October: http://www.mamapedia.com/questions/16908621786722336769
You wrote that she has tantrums, she interrupts, she never stops talking, and she's such a handful. Is that how you think she offended the other girl? Maybe she just hasn't learned any skills for managing her own behavior, so maybe her behavior is more than "unintentional" and just poorly controlled?
Some kids aren't affectionate and don't like to be touched. You say here that's how she is. What is your reason for wanting to change it? Sometimes it's personality, sometimes it's a sensory issue.
But based on your other questions about this child and your desire for parenting classes, I honestly don't think the lack of demonstrativeness is a big problem. I think your concerns about a better structure for parenting both children is more essential. Once you get things under control, I imagine her behavior at school and her ability to socialize appropriately will fall into place.
I think it makes sense to talk to the teacher in a conference about behaviors she is seeing at school and what the triggers are. You'll be better able to see a pattern if you talk to the person who sees her all day and find out what disciplinary techniques are most successful.