That would depend on the tenancy recited in the deed to you and your husband. If a joint tenancy or tenancy by the entirety was created in your deed then he would become the sole owner of the property upon your death. He could then make his own will and leave the property to his own relatives when he dies. If there is no tenancy recited on the deed or it provides that you will hold the property as tenants in common then upon your death your interest in the property may be shared by your children and your husband according to the laws of intestacy in your state. Your children may receive nothing depending on the value of the estate. Alternatively, if the property is owned as tenants in common you could leave your half interest to your children in your will with a life estate to your husband. That way he could continue to live on the property and when he decided to sell or if he died your children would receive half of the proceeds of the sale of the property. You should seek the advice of an attorney to discuss your options.
If no one else's name is on the deed you would get it.
Yes. All the children would be considered heirs at law under the laws of intestacy. See related question link provided below.
No. If your present husband is the father of the children of his previous marriage and is the custodial parent he would have to sue his ex-wife (the children's mother) for support.
Your husband cannot get joint custody of your children from a prior marriage. Custody arrangements are made between parents of children. Your present husband can legally adopt your children with their father's consent. He would then have all the legal rights and obligations of a biological father. The children would become his legal heirs-at-law.
Any property that he had will become a part of his estate. Usually the spouse will inherit it all, but there may be some provision for parents to inherit part of the property if there are no children. A will is important! And you would need to consult an attorney in Texas for specific rules.
An "uncle by marriage" would be your spouse's Aunt's husband.
You love them as you would love your husband or wife. You treat them with respect, as indiviuals who have feelings just like us. You treat them the way you will treat the child that you are your husband have.
Your husband should be paying child support for his children unless the mother of the children has remarried and her new husband adopts the children. It would be wise that he gets each child DNA tested to even be sure they are his children. If your husband did not let you know before you married him that he had four children then it's an injustice to you, but the two of you have to learn to communicate and decide on what the right recourse is to resolve this problem.
It would go to his spouse
Only if he owned the house before your marriage. If the house was purchased during the marriage, you should be part owner and he would not be able to sell the house without your approval.
You would be their Aunt (by marriage).
I assume that you are the sole owner of the house. You would need to check your state laws of intestacy to determine what your husband's rights would be if you died intestate, or, without a will. On the other hand, you could provide your husband with a life estate in your will.