Charge conjugation parity ($CP$) symmetry violation is linked to important physics questions such as the matter-antimatter asymmetry and the Strong $CP$ Problem. Tabletop precision measurements using heavy atoms and molecules can set stringent bounds on the new physics that attempt to explain these problems, and these measurements are complementary to direct searches of new particles using colliders. Radium, among other radioactive elements, is a sensitive probe to hadronic $CP$ violation due to its heavy and octupole-deformed nucleus, and the sensitivity is further enhanced by incorporating the radioactive element in a molecule. In this thesis we introduce the first laser cooling of radium-226 ions and measurements of the low-lying $^{226}$Ra$^+$ energy levels. We realize control of the radium ion $S_{1/2}\rightarrow D_{5/2}$ optical qubit for implementing the quantum logic spectroscopy technique to prepare and readout the radioactive molecular ions. We also present production and detection of radium-containing molecular ions that are sensitive to hadronic $CP$ violation. Finally, we discuss ongoing work on designing a hadronic $CP$ violation experiment using radioactive molecular ions and developing a long-term source for the short-lived radium-224 and radium-225 atoms.