Kira wants to know: What is some sort of issue for my MC to deal with as a result of her grief that would be easy to write in several scenes? I need her to have a more fleshed-out internal journey.
At the risk of sounding macabre, your very question gave me a great idea for your MC. You mentioned "fleshed-out" journey....and, well, what I'm going to suggest would literally be one.
Your heroine fits the bill. She's lost her mother, and I can probably assume they were very close. You didn't mention how long it had just been the two of them before her mother remarried the step-dad, but it's probably pretty safe to say that her mother was the girl's world. Depending on the circumstances of her father's absence (either through death, divorce, suddenly deserting their family, etc), your heroine might actually have a very hard time reconnecting with any father figure, much less a "fairly new" one.
To add insult to injury, the step-father removes the girl from her support network to "start over." This is great fodder to push her over the edge a bit and overwhelm her current coping strategies. Friends are especially important to teens, and for the heroine to have to leave her school, church, sports leagues, etc., to live with a man she doesn't really know (or want to know) that well, this could certainly drive her to seek an emotional release from her thoughts, fears, and anxiety.
So you can write the scenes realistically (I doubt it'll be easy writing, as this is really difficult stuff), I'll go over what I understand about self-harm.
1) Self-harm can take on many forms. It typically starts with a razor blade or knife at first, but it can progress to burning oneself (with erasers, car lighters, cigarette buttes), pulling hair out, picking wounds, or hitting oneself.
2) Self-harm is purposeful without the intent to kill themselves. If the person actually wants to die, then they move up the ladder from self-harm to suicidal ideation or suicidal attempts.
3) Self-harm has many motivations. Some of the most common are listed below.
A) The person wants to distance themselves from emotional pain/numbness. Cutting (or self-harm) is a way to feel something in a controlled way. When people are overwhelmed with negative emotions, the out-of-control chaos of a person's mind can be frightening. Don't think of people cutting themselves in a frenzy. It's actually calm, calculated. It can help distract a person from what their going through internally.
B) The person is expressing something for which they have no words. Literally, the term for this is alexithymia ("no words feeling"). There just isn't a label to use to express how they feel. Cutting themselves can display anger, show emotional depth of pain, and shock others. It can also get them help without actually having to ask for it (if a friend were to see an uncovered arm of someone who cuts, they would be extremely concerned).
C) The person wants to experience a sort of euphoria. The body is a wonderful thing. When being hurt or injured, it works to minimize pain and heal quickly. The brain releases endorphins that work as pain-killers when the body is hurt, regardless of whether that hurt comes from oneself or another. This physical high can be addictive, but the body does build a tolerance to endorphins and the subsequent acts of self-harm won't produce that initial "high." This can lead to more severe self-harm, such as deeper cutting or moving on to a more dangerous form of self-harm.
D) The person feels like they deserve to be injured. Either they think they are "evil" or that they should be punished for some misconception over whatever has happened as being their fault. They might think that they deserve the pain, and that maybe somehow in hurting themselves, it will stop a worse punishment later from someone/something else.
E) The person wants to heal emotionally by taking care of their physical injuries. When emotions run to deep and out-of-control, self-harm provides a way to make the internal pain external. When you care for your cuts and bruises, it's a way of taking care of internal scars. There are some people who have rituals to take care of their body after self-harm occurs, making the aftercare more important than the act of cutting or self-harming.
Here is an excerpt I found online from the book Cut by Patricia McCormick that kind of gives an idea of the internal mindset of a cutter:
“Then I placed the blade next to the skin on my palm. A tingle arced across my scalp. The floor tipped up at me and my body spiraled away. Then I was on the ceiling looking down, waiting to see what would happen next. What happened next was that a perfect, straight line of blood bloomed up from under the edge of the blade. The line grew into a long, fat bubble, a lush crimson bubble that got bigger and bigger. I watched from above, waiting to see how big it would get before it burst. When it did, I felt awesome. Satisfied, finally. Then exhausted.”
I wish you the best with this book. Teens need to understand that just "regular Janes" can develop this scary behavior.