If my wife commited adultry, can I get the house and half custody of the kids?

I am so sorry for your situation.  Adultery is what is considered to be a "fault" ground for divorce that has to be pled in divorce papers and proven in court to obtain a divorce.  It does not bear any weight - in the general sense - on the division of marital property or custody of the kids.  You assets are divided under the theory of "equitable distribution" and the courts often favor joint custody of the children but that determination is always made "in the best interest of the children."  Good luck.