You have to file a separate tax return for each child. You cannot include their income on your tax return. Their UTMA transactions and income go on their individual tax returns, not on your tax return. You go through the "Child's Income" section on each of their tax returns, not on your tax return.
You said that the children's UTMA accounts have capital gains "which are more than offset by capital gains losses that I have." Your capital losses cannot offset the children's capital gains. Their capital gains go on their tax returns. Your capital losses go on your tax return.
Their is an option to report a child's income on the parent's tax return. You cannot use that option because the children have capital gains. It's usually not a good idea to do that anyway. The only advantage of reporting the child's income on the parent's return is that it's less paperwork. It will not save any tax, and in many cases you could end up paying more tax overall than if you file separate returns for the children.
