If you pay for more than half of their support (and meet all of the other requirements for claiming a dependent) then yes, you can still claim them even though your children have investment income.
How you report this income largely depends on how much it is. It sounds like you may be subject to the "Kiddie Tax". Please see below for more information regarding the Kiddie Tax and your filing requirements:
https://ttlc.intuit.com/replies/3301446
https://ttlc.intuit.com/replies/3302004
