I hear your dilemma, at the same time, would moving your meds, create havoc on your normal routine? I keep mine in my bedroom, and one bottle in my purse. That's a location that works for me. When I was on MS meds, I kept them, in the fridge, as ordered and had a needle disposal container on top of the fridge. Kids, stay away...period.
I grew up, around meds, not for MI but physical health issues, and developed a healthy respect that it's safer to not touch such meds, they can cause health issues if they aren't meant for you. My gram, keeps hers in her kitchen cabinet, always has, probably always will. My late stepdad kept his meds on this little table area, near the dining room table. Various locations, work, for different people.
You'd teach your children to stay away from blood pressure meds, blood thinners , insulin...same can be taught about your meds. They could get really sick, if they took them.
Thinking some more, keep that lock on that drawer, anyhow. Gives a moments pause, that that is your/mommy's drawer.