Two people are married?

Different states, different countries, different laws. I'm not aware of anywhere that allows the remaining living partner to "adjust" the deceased partners will. 

If someone dies intestate (w/o/ a will) their spouse is assumed their legal next of kin and will inherit the entire marital estate. This would in most cases cut out any other family members. But wills are set in stone at the time of someone's death so if partner B outlived partner A partner B couldn't somehow change partner A's will. If partner A drafts a will that leaves their spouse out entirely it would only convey to non spouse relatives assets that are owned in toto by partner A, meaning no jointly held marital assets could be granted to someone else. But in the case of a joint marital asset like a house partner A could in theory bequeath his/her half of that marital property to non marital relatives. Then those non marital relatives would own 50% of the property in joint with surviving partner B. 

But seriously, go talk to a lawyer about this stuff. 

If a husband or wife dies with no Will, the remaining spouse gets what is left behind. Unless there is a life insurance policy left to someone else, then that isn't included

If there is a Will, it can't be legally changed.  The estate is dispersed according to the wishes of the deceased spouse as stated in the Will.  

Assume you mean that A & B have separate 

wills (if any wills at all). How it goes depends 

somewhat on where they live, but generally: 

Situation 1, partner B gets it all and can do 

whatever they want with it (there is no "cut 

out all family", since B automatically gets it 

all anyway). 

Situation 2, partner B gets only what the will 

of partner A specifies. There is no way for B 

to (legally) adjust the will, since its "executed" 

immediately upon the death of A.

I am not a lawyer in your jurisdiction.  Here case 1 is called "Intestate" and there is a set of rules that will determine how the assets are divided.  Partner B has no say in that.  They can distribute their share if they wish.  Partner B cannot alter partner A's will. They can challenge it if it doesn't meet legal requirements.  Here the will would be challenged if they don't make adequate provision for anyone they are closely associated with.

1. If one spouse dies before the other and there’s no will, everything goes to the spouse so B can keep everything. It’s up to B how to distribute the property. 

2. If A dies and the will says that the kids get she says in the will then the kids get whatever is on the will. All the remaining stuff will go to B since he’s the next of kin. B can’t change it to give everything to himself because only the person that wrote the will can change the will. 

If A and B both die, A’s will gets executed so stuff will go according to what’s on the will. B’s stuff will go to the next of kin, so kids first. If there’s no kids, then it goes to the parents or siblings (not sure who takes precedence but I think it’s the parents). Then the cousins. No cousins then it goes down the line. At some point it’ll just go to the state and the state will sell it, auction it, or whatever.