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If you are the custodial parent (the kids lived with you more than 1/2 of the year) then you would be entitled to claim them as exemptions.
how can I stop him from claiming themYou can't. If he claims them and files first your return will reject and you will need to file on paper. The IRS will process it and then inquire of both of you to determine which return is correct. If you support that you are the custodial parent, yours would be the return they allow the exemption on.
Suggestion: File as early as possible. If you file before him, his return will reject and he will need to paper file if he wants to continue the issue.
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