To do a paternity test they would need a DNA sample from the mother, the child, and the potential father. Since they did that test with JG, that test would have a clean sample of Caylee's DNA for comparison to other items. Normally it would be difficult to get a DNA sample from a missing child. They would be forced to use items like hairbrushes or toothbrushes to get a sample of the child's DNA to use for other testing, and those items may not yield a full DNA profile, and could have been used by other people giving a contaminated sample. In addition, in this case where there is no identified father, attempting to get a full profile would be extremely difficult. I think we saw this when the first hair came back with the death band. Because they could only use mDNA testing, they could not determine for certain if the hair was Caylee's or KC's. Of course, since KC was alive and well, it would need to be Caylee's, but they could not tell for sure without another hair that was definitely Caylee's to compare.
The paternity test would have included an irrefutable sample of Caylee's DNA, hers and only hers. Most paternity tests that I have heard have the samples obtained under controlled conditions (i.e. with a doctor present) so there can be no questioning of the authenticity of the samples. I think that is why they sent it.
The other testing would include DNA found on things like the stains in the trunk, the shovel, stains in AL's vehicle, debris in the truck, bodily fluid stains on KC's clothes in her closet, etc.
Does that help?