If the money was in a Roth IRA when the divorce was finalized, it doesn't matter where it came from before that.
You need to get your share transferred into a Roth IRA in your own name. If this is not already done, you need to get a QDRO (qualified domestic relations order) from the court and give it to the Roth IRA custodian. This will order the custodian to move some of the funds into an IRA account in your name. Your ex can probably ask to transfer the funds without a QDRO from the court as long as the divorce order has the right language. The transfer has no tax consequences for either party if done correctly.
Now that you have money in a Roth IRA in your own name, the following rules apply:
If you withdraw funds before 5 years, you owe regular income tax on the earnings, but not the contributions. Even though your ex had the Roth IRA more than 5 years, the holding period does not transfer to you. You have to restart the 5 year clock when you open the Roth IRA. There is also a 10% penalty if you are under age 59-1/2.
The contributions and rollovers should be allocated proportionately. For example, suppose the Roth IRA was funded with a $100,000 rollover from a 401k, and is now worth $150,000, and you get half. You would get $75,000, of which $50,000 is the rollover and $25,000 is earnings.
Roth IRAs are always withdrawn contributions first. So in this example, if you received $75,000 in a Roth IRA and needed to withdraw $40,000, that withdrawal would all be from contributions and would be tax-free. The remaining account balance would be $10,000 of contributions and $25,000 of earnings, which would be important the next time you withdrew money.
If you withdraw funds after 5 years and are under age 59-1/2, you pay income tax plus a penalty on the earnings portion. If it is after 5 years and you are over age 59-1/2, all withdrawals are tax-free.
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Because the 5 year clock resets for you, and if your ex is willing to cooperate, your ex could withdraw an amount of money and give it to you, and probably pay no income tax themself.
My suggestion is that you ask your spouse for the amount of money you are likely to need over the next 5 years to be paid to you by him withdrawing money from his account, and the rest of the money be paid to you by having him tell the IRA custodian to transfer the remaining amount into a Roth IRA in your name.
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However, if I was your spouse, I would simply have the IRA custodian transfer the entire amount I owed you into a Roth IRA in your name. That way, the money would belong to you only and any taxes due from a withdrawal would be your responsibility and would not affect me. Then once the money is in an Roth IRA in your name, whether or not you owed any tax on withdrawals would depend on whether you were withdrawing contributions, rollovers, or earnings.
