Can I disown my heir?

On your first question: disinheriting your heir is not possible unless you have elective succession. Then you change for example choose to elect your second or third son. Most of the time your vassals will elect the person you elect. Off course there is a chance they will elect someone else, so it's tricky.

On your second question: yes, it is possible. I have done it before (horrible me) when I was in kinda the same situation as you. My heir died relatively young and so his only son became my heir, but had really bad traits. So I plotted against my grandchild (who was about 4 years old) and managed to successfully kill him. There is a catch however, which happened to me. The plot was successful but the truth came out that I did it, so I got the Dishonorable trait and, even worse, the Kinslayer trait which gave me massive relationship penalty to my family and vassals. So yes, it's definitely possible but there are some serious risks.

I haven't tried to plot against a child, but I have tried to assassinate a child. After about 10 failures at a supposed ~50% success rate, I have the sneaking suspicion that CK2 doesn't condone the intentional deaths of children. Also, I am a horrible, horrible person.

(The other theory is that the game lied; perhaps it told me the success chances against the child, but actually rolled against the guardian or some other adult in the area. I also did some save-scumming; if CK2 saves the random seed, then I may have just been failing the same 3-4 assassination attempts in a row due to loading the "same" random numbers.)

it IS possible to kill your children, but when cought you will know why it's a bad idea to try and do this.

however, sometimes the future of the realm is more important then honourable family relations.

This is why i love elective succession to much, the ability to pick your heir without having to kill anyone. (hint: if you dont have dukes, you are the only elector!)