Molecular dynamics simulations are utilized to investigate the interactions between the skin cancer drug 5-fluorouracil (5FU) and peptide-based dendritic carrier systems. We find that these drug-carrier interactions do not conform to the traditional picture of long-time retention of the drug within a hydrophobic core of the dendrimer carrier. Rather, 5FU, which is moderately soluble in its own right, experiences weak, transient chattering interactions all over the dendrimer, mediated through multiple short-lived hydrogen bonding and close contact events. We find that charge on the periphery of the dendrimer actually has a negative effect on the frequency of drug-carrier interactions due to a counterion screening effect that has not previously been observed. However, charge is nevertheless an important feature since neutral dendrimers are shown to have a significant mutual attraction that can lead to clustering or agglomeration. This clustering is prevented due to charge repulsion for the titrated dendrimers, such that they remain independent in solution.