HI dBrown1611,
I am so sorry to hear of your's and their loss. If the children under the age of 19 and you are considered their parent, you will have no problem in claiming them as a dependent on your end of year tax return, as long as no one else believes they have a justifiable reason to claim their Social Security Numbers on their tax return.
While the worst case scenari would be to paper file that tax return and not electronically file it, efile should go through as long as you are considered their parent or their legal guardian.
Read further under "Why claim someone as a dependent?"
https://turbotax.intuit.com/tax-tips/family/rules-for-claiming-a-dependent-on-your-tax-return/L8LODbx94