No it is not 'normal'. Normal implies that we
must do X.Y.Z. in order to fit some idealized mold of what humans are supposed to be.
In this case these are all typical behaviors of grief - all of them, how your family responds, how you respond even how strangers will respond in various ways to the 'news'. It is all typical.
There are five stages to grief - this is typical of the human condition:
http://en.wikipedia.org/wiki/K%C3%BCbler-Ross_model
Basically:
Denial, Bargaining, Anger, Depression, Acceptance.
Some people can actually go from denial to acceptance in short order, others have to take a much longer route through each. Others will hit a snag and go back and forth between Anger and Depression (or bargaining and anger, or Denial and depression).
All of these stages can be expressed in a lot of different ways depending on the individual.
EXAMPLE: I respond to depression with laughter - yes I know it seems irrational and illogical and contrary to what the majority think of as depression - however its my 'coping mechanism' to deal with the sorrow. I also deal with fear with laughter (humor), Anxiety with Laughter, even anger with laughter (this is often in the form of sarcasm). Its all part of my coping mechanism which works for me to cope with the plethora of emotions and 'survive' until the end of whatever it is I am going through.
You sister is responding to what she feels in her own way. Most likely she is calling upon her tried and true coping mechanisms and you are seeing those at work. Mom is dealing in her own way, Grand-folks in their own way - everyone who is touched by this event is at a different stage of grief and coping the very best they can.
Yes indeed, their ways of dealing with this will affect how you feel, thus you will get secondary and tertiary emotions, such as this feeling of rejection you are feeling. I seriously doubt they are doing it on purpose.
Your Cousin may be expressing pain a bit more clearly than you thus appear to need the support/comfort of the others more. Most likely being an adult male you are wearing your 'Man Mask' and not exactly showing how much this hurts you.
I suggest you try to find ways to express what you are feeling in a healthy manner. Trust me, standing up in the middle of the room screaming profanities and throwing objects is not exactly a healthy way to express stuff. Pulling people to the side and putting your emotions to a few words is more healthy.
This too shall pass. As long as you are a relatively healthy person you will process through all of these emotions and will eventually hit 'acceptance' and start moving on. No acceptance does not mean you will forget or feel 'happy' over this. You will, undoubtedly, have moments of relapsing severe pain, something will trigger the emotions of loss you feel - but those moments will come farther and farther apart and the sting of hurt will greatly reduce through the years.
You are OK, and your family is OK. While nothing here is 'normal' it sounds like its all pretty much typical and even presenting in healthy forms of expression of the greif process.