You will not be guilty of abandonment if you leave the home because there is no such thing as abandonment in divorce law. Don't feel bad, most non-lawyers ask the same question. As for custody, you are free to take the children with you until a judge says otherwise.
I believe you mean abandonment. Antonement has religious connotations. You can leave and you can take your children unless there is an order forbidding you from doing do. You really need to speak with a lawyer ASAP.
Yes, you will not lose the rights to the house if you leave. The home is marital property if it was acquired during the marriage. Moving out will not change that characterization. However, there are some good reasons to stay in the house, if you can, depending on the circumstances. Talk to a lawyer, divorce is a difficult process and you shouldn't go through it alone. Do you have a place to move to?