Spacial and aggression questions

DD is two and she has some issues when it comes to her space and others especially kids, which I understand is normal for her age, however we are not talking a 5-10ft radius in her case; we go to the park big or small and if we are not the first ones there or other kids come along she screams "no" and/or "mine" over and over and gets upset, same with the library, church, any public place really. This has been going on for a long while, also happens when a child enters the house occasionally (we don't have company often). Is this typical for an SPD who is two?

Also, she picks aggression either towards others, herself or objects when she starts to get thrown off in any situation - me, OT, PT, ST, my folks, and the kids at school, inside places when she settles into a routine or is "protecting" her space. This is a daily if not multi-daily occurrence. She even raises her hand as to hit at times if she does not just hit right away. OT said months back that her raising her hand is a good sign as she is giving someone "a chance" to step back - but these kids and adults are doing nothing wrong except trying to correct behavior or sit and do a neuro typical functional activity (so I see where it is "wrong" in her mind maybe). Why aggression? Behavioral and/or developmental therapy has been brought up if/when ST is dropped, should I be talking to someone about the aggression issues and what it may mean?

Thanks - it is just a tough battle somedays because she can be really sweet but if she is thrown off, like touching her stuff or what not, watch out. FYI - she often just choses to shut down at school, plays by herself, doesn't talk much, etc. I am told when she enters more structure she will participate more.