Grandparents and parents have the same standing to claim children/grandchildren under the tax law, except in certain tie-breaking situations that do not concern us here. If you had the children in your physical custody for more than half the nights of 2018 (the nights don't have to be consecutive) then you are the custodial parent for tax purposes.
(The IRS defines custody based on where the children physically live, regardless of any court orders.)
If the children lived with you more than 183 nights, then you are the only person with the automatic right to claim them as dependents. You don't need form 8332. You will answer they lived with you more than half the year and that you aren't waiving/releasing their exemption. The need for form 8332 should not come up, if it does, you answered something wrong. You are entitled to the child tax credit, EIC and head of household (if you meet the other qualifications.)
Neither parent can claim the children this year under any circumstance. Both of them are "non-custodial" for 2018. Since you are not a parent, you can't issue a form 8332 that would allow either parent to claim the children. Because you had physical custody more than half the year, you are the only person who can claim them and no one else can claim them even if you don't.
If one of the parents does claim the children, that may block you from e-filing. Print your return and mail it in. If there is a duplicate claim, the IRS will eventually investigate. You may need to provide proof that the children lived in your home more than 183 nights of 2018.
