My ex has once again claimed one of our children. Both children live with me 80/20 and I also carry the insurance on them. Question is how can I stop him?

How do I get my money back?

If you feel strongly enough, you could go to Family Court and get a Cease and Desist order.

What will that do?

If he fails to comply, he could be fined and/or arrested.
If you have a job, change your withholding  so that you do not have to wait for a refund at tax time.

I get that, but would it get my money or just stop him from filing in the future

Nothing stops you from "getting your money" reguardless if he files or not.  It is just an inconvenience that you must paper file and answer future IRS letters.   He will eventually have to pay back any refund he received for falsely claiming the child, plus interest and penalties.     A BIG tax bill will probably stop it.  (He should amend not to prevent the interest and penalties).

If a dependent that you are entitled to claim has already been claimed by another taxpayer, your e-filed return will reject since the child's SSN has already been used (either intentionally or in error such as a mistyped SSN).

Your only recourse is to file a correct tax return, claiming what you are entitled to claim, then print and mail the return.

The IRS will process both returns and pay any refunds.   Shortly (within a year) the IRS will mail letters to both taxpayers asking if their tax return was filed in error and suggesting that they amend if they improperly claimed the child.

If neither taxpayer amends, the IRS will send a second letter asking for each taxpayers proof that they are entitled to claim the dependent, such as proof that the child physically lived with them more than half the year.   School records, child care records, household receipts, medical bills, etc., that show that the child lives with you should be retained.

The IRS will evaluate each taxpayers claim and award the dependent to one taxpayer, the other will have to payback any refund received plus interest and possible penalties.   The parent that had physical custody usually always wins.

Do not ignore the letters or you will loose.