If you purchased the beach house during the marriage it is marital property and subject to distribution. North Carolina does not give credence to whom the property is titled to, or whose name is on the mortgage when dealing with marital property. There could be a separate component to the house depending on who owned the beach trailer before the marriage. However most courts will say that proceeds from separate property which are used to purchase a home (or other property) during the marriage will be deemed a gift to the marriage, thereby making the beach house 100% marital.
With respect to custody courts always look to the best interests of the child to determine the custodial arrangement. With a child as young as your son I would agree that you have a good chance in being awarded primary physical custody if you can demonstrate that your son living in one home is in his best interests. Many judges will be hesitant to order a split schedule for a child so young as it is.
The cars your older children drive can be considered marital property if they are titled to you and your husband. You can however present evidence that shows the intent was that these vehicles are the property of your children, and the court may exclude the vehicles from the marital estate.
If you and your husband agree to place the home on the market prior to the distribution of property you can put the home on the market now, but you will need both or your signatures to do so. The mortgage payments will not affect child support as child support is based on income, medical insurance costs, and daycare expenses only. Child support does not take a parent