I think it is a wise idea to not rush back into weighted deadlifts/squats. Slow progressions will be best. IMO you are looking way to advanced for your exercise selection with core development. I really feel you need so go to somebody who will give you a full functional assessment and has an excellent grasp of muscle synergistics, biomechanics, etc. to determine exactly where your limitations and weaknesses are. The more advanced exercises may seem more demanding, but you are likely not activating the proper musculature and patterns due to your body likely not being able to handle the increased difficulty of the exercises. This will only lead to further imbalance and injury.
Also, if you tend to injure your back every time you try to build strong glutes/hams, going "too heavy too fast" may be part of the reason but there are several things to consider:
1) Do you have the proper muscle activation from the prime movers to perform those lifts at that load? If the hamstrings and more importantly the glutes are not activating properly, the lumbar spine musculature will take on the added load.
2) Do you have the proper muscle activation from the secondary stabilizer musculature? If the lumbar spine stabilizers cannot support the lumbar spine properly and you are performing lifts like deadlifts and squats, than regardless of gluteal/hamstring activity, the lumbar spine won't be able to sustain and support the load, resulting in injury.
3) Do you have the needed mobility at the hips, ankles, Tspine, etc to safely perform the lifts? Lack of mobility at one place (ie: the hips) will be counterbalanced by increased mobility at another joint that likely shouldn't take on that mobility during that motion (ie: Lumbar spine).
4) Are you choosing the best exercises for the goals you want with the current abilities of your body? Squats and deads are great, but if your lumbar spine can't handle those shearing loads, you may be better suited to perform other hip dominant exercises (hip thrusters, single leg variations, etc).
Any chance of static postural photos? Or better yet, dynamic video of exercise technique?