Lottery winnings during marriage are typically considered community property and are divisible at the time of divorce. The Judge has the right to make a just and right division of the community property at the time of the divorce. It does not have to be 50/50 in every case. You could make the argument that you had already separated and divided your assets prior to winning and, while the winnings may be community property, the Judge might award them to you.
Every court is different, so talk with a good family lawyer in your area to see what the Judge in your case might or might not be willing to do. Also discuss the exact facts of your purchase of the ticket, and what funds you used to buy it, to make sure there are no special circumstances in your case that could affect the characterization of the winnings.
The winnings would not likely be considered income for child support purposes. Any interest or income generated by the winnings could be, but while $10,000 is a sizable jackpot, I don't think it is big enough to generate enough income to change your child support.
Congratulations on your win! Whatever the case, be careful not to spend more in attorneys fees arguing over the winnings than you actually won. Half of a "free" $10,000.00 is better than giving all of it to the lawyers in the case.
All property accumulated during the marriage is presumed to be community property. Even if you are separated, if you remain married then property continues to be accumulated as community property unless you have a valid enforceable partition or postnuptial agreement with your spouse. You would have the burden to prove that you acquired the lottery ticket with separate property funds to be awarded 100% of the winnings as your separate property.
However, the Court does not have to divide all community property on a 50/50 basis. The Court may accept an equity argument that you should be awarded all or a larger portion of the lottery winnings.
The lottery winnings are divisible by the court, to the extent they are in existence at the time of divorce. If you have not filed for divorce yet, you could spend that money on living expenses, hiring an attorney, etc. and there may be nothing left to divide at divorce time.
The court will not take lottery winnings into consideration in setting regular child support. A one-time bonus like that is treated as property, not income (except by the IRS--it's all income to them).
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