Hamstring, glute and back strengthening yoga poses can be used to strengthen the muscles along the back of the legs and spine body in both forward bending and backward bending positions.
While doing forward bends for the hips you can strengthen the hamstrings while they are lengthened. You'll be stabilizing the hips and that in turn will give the muscles at the back of the spine a foundation for contracting and bending the spine backwards.
Weight lifters use weights to strengthen muscles. Doing yoga poses we can use the weight of our body to strengthen our muscles.
In a standing forward bend you can strengthen the hamstrings and glutes by using them to support the weight of your upper body.
How do you make your glutes and hams support the weight of your upper body? One way is by taking your hands off of the floor. If you take your hands off of the floor slowly (first relax them, then lift them) you may notice an increase in tension along the back of your thighs. You can try increasing the tension deliberately. You can also try deliberately activating your glutes. Vary the tension between hamstrings and glutes. You may find it more comfortably on your hamstrings if you try to add more tension to the glutes so that your hamstrings don't have to work quite so hard.
If you want to stretch your hamstrings while keeping them and your glutes active then tilt your pelvis forwards. You can then try to bend your spine backwards.
With your hamstrings and glutes stabilizing your pelvis relative to your thighs, you then give your back muscles a foundation for backbending your spine. You can strengthen the spinal erectors at the same time.
If you want to give your back muscles (and glutes and hamstrings) a rest then place your hands on the floor or on your legs to support the weight of your upper body.
The hamstrings are the muscles at the back of the thigh. (The picture to the right shows them from viewed from the back.)
They attach to the pelvis at the sitting bones and one way to activate them while doing a standing forward bend is to focus on pulling down on the sitting bones. Try to pull down in such a way that the back of the thighs engage.
To give the hamstrings more weight to work against, engage the spinal erectors by bending your lumbar, thoracic and cervical spine backwards. (These muscles run up the back of the body on either side of the spine. They run all the way up from the pelvis to the back of the skull.)
When bending the spine backwards, the more you contract the spinal erectors the more you bend the spine backwards. Try to gradually increase the contraction and then gradually release. You can contract while inhaling and release while exhaling.
To take the hamstring through a fuller range of motion, start in a forward bend with hamstrings and glutes and spinal erectors activated. Shift weight to one leg and lift the other leg rearwards into the yoga pose called warrior 3.
Focus on your foundation first, the supporting leg and spine. Make sure the back of your standing leg and spine are engaged and then focus on lifting the lifted leg higher by increasing the tension at the back of the lifted leg.
Because this is a balancing yoga pose, I'd suggest that you focus on moving slowly and smoothly. When first doing it don't worry about breath synchronization. Instead focus on continually breathing slowly and smoothly while gradually moving into (and out of) the posture.
As you balance improves, you can work your standing leg a little bit harder by reaching both arms forwards. Your hips will have to shift back to stay balanced, which, if you keep the same pelvic tilt, lengthens the hamstrings of the standing leg even more.
In a seated forward bend, you can strengthen your back and your legs by pressing your legs down, and reaching your arms forwards. The further you reach forwards the harder it is to bend your spine backwards so in this case you are strengthening the spinal erectors while they are lengthened.
If you can grab your toes, or the sides of your feet, you can use the muscles at the back of your legs against the muscles at the back of your spine against each other to increase your forward bend.
Use your leg muscles to press your legs down and use your back muscles to help pull your arms up.
So that this helps your forward bend, make your arms and back slightly stronger than your hamstrings so that your chest moves closer to your thighs as you hold this pose.
In high lunge you can practice activating back of the body muscles in a shortened position. On the inhales lengthen and open the front of your torso and hip (back leg hip.) On the exhales engage spinal erectors and glutes and hamstrings of the back leg (imagine trying to lift the back thigh.)
Relax the back of your body while inhaling.
You can also practice strengthening the hamstrings with knees bent in the yoga pose called bridge.
In this pose, you can concentrate on using the back of your thighs and your glutes to push your pelvis higher. Inhale activate and exhale relax slightly. If you want to use your arms (and strengthen your shoulders and back) then place your elbows on the floor with forearms vertical. As you press your feet down (using the backs of your thighs) push your elbows down into the floor to open your chest at the same time.
For more on using the muscles at the back of the body check out Spinal Back Bending Exercises which includes exercises for bending the spine and hip backwards in isolation (from each other) and Spinal Back Bending Yoga Poses which includes yoga pose that integrate back bending actions of the spine with back bending actions of the hip.