Your anterior core can never be strong enough. For the core-engaged dead bug, lie on your back with the hips and knees flexed to 90 degrees, and then pull a light band over your core/torso to engage the abs.
Exhale hard to get the ribs down, and think about "rolling" the pelvis back. Your back should be flat and pressed into the ground. From this position simply extend the hip and knee, focusing on keeping the back flat throughout.
When do you do low reps and heavy weight? What about higher reps and light weight? Read this and finally feel good about writing your own training programs.