According to Georgia law, you would share title to the house with your husband's children if your husband died without a will. You would get at least one-third of your husband's estate in any case.
Here's the actual text:
Upon the death of an individual who is survived by a spouse but not by any child or other descendant, the spouse is the sole heir. If the decedent is also survived by any child or other descendant, the spouse shall share equally with the children, with the descendants of any deceased child taking that child's share, per stirpes; provided, however, that the spouse's portion shall not be less than a one-third share;
This issue is the kind of thing that can really divide families, because how do you split a house in three? I'd suggest that your husband make at least a simple will, directing to whom the property shall pass.
You and the child would share the estate equally. However, you would be authorized to file a petition for year's support and would ask that the house be awarded to you. It would be up to the probate judge as to whether you would be awarded the house.
This answer is not intended to give you specific legal advice regarding your situation, or to create any attorney-client relationship.
Under Georgia law, if your husband is the sole owner of the house and he dies without a Will, leaving you, as his surviving spouse, and one or more children who survive him, then you and each child would take an equal share of the house (and any other assets which become part of your husband's probate estate), provided that you would get no less than a 1/3 share. You, as the surviving spouse, could make a claim against the probate estate for a "year's support." However, the right to a year's support is not a right to any fixed share, and if the children contest your claim for year's support you may not receive the entire title to the home. The court will look to your other assets and income as part of making the decision regarding how much to award you.
It is not entirely clear from your question exactly how many children are involved or whether any of them are still under 18. If there is any child who is under 18 at your husband's death, the minor child can also make a claim for a year's support. That may decrease the possibility that you would receive the entire house as part of a year's support claim.
Your husband needs to do some estate planning as soon as possible, preferably with an experienced estate planning attorney who has dealt with a large number of blended families. You should also consider your own estate planning, to make sure any assets you have end up where you want them to end up. Please note that it may not be possible for you and your husband to work with the same attorney, depending on your respective estate planning desires. But you need to start the process, or neither of you is likely to end up where you would want to be in the event of either of your deaths.