I suggest you try hip thrusts. You may do hip thrusts,  low bar back squats and rdls twice a week. These are technical exercises, make sure to aim for quality of movement.  Start light, slowly progress to a challenging barbell weight only when you are satisfied with your technique. I know it is expensive but a trainer by your side would be great for safety and faster results. Please consult your physician before any workout program if you have not already done so. Be consistent, results will come.

Omer

I'm sending a leg/glute workout you can try. Glute And Core Toning

I don’t have such a program yet, but I’m working on it.

You can safely try these 3 workouts I created:

Posture workout

Healthy Spine

Bad Back

Omer

Never give up!

You must do some strength training to increase your metabolic rate. Twice each week will be good.

Fast flowing workouts with light to medium weights will be beneficial. You may want to try:

Total Body Metabolic Conditioning

Difficulty: Moderate

Duration: 36:19

2in1 Hourglass Abs & Booty Pump

Difficulty: Intense

Duration: 10:14

Killer Cardio AMRAP

Difficulty: Intense

Duration: 19:03

30 Min Low Impact Full Body Workout

Difficulty: Moderate

Duration: 35:49

If you have access to gym equipment, you may want to try this:

Gym Cardio
Duration: 4 Weeks
Workouts: 19 Workouts
Difficulty: Intense

Omer

I always remind myself that working out has to be like brushing your teeth; You have to keep on doing it regularly as long as you live. As a side effect, you will see great physical changes. Of course the grand prize is good health. One doctor wrote “If we could bottle and sell exercise as medicine, it would surely be the most sought after and most expensive drug”. Enjoy.

Ömer

Your lower back must be first priority. Do not panic but see your physician asap. Learn safe exercises to strengthen your abs and obliques. Start with core exercises, the simpler the better. 

Lower back problems can range from simple to very dangerous. Whatever you do, do not exercise neglecting pain and discomfort.

I suggest you to not rush it. Start slowly. Choose two or three short (10-30min) workouts you enjoy and repeat them weekly for a month or two. Walk as much as you can. Switch when bored.

Everyone knows that dieting is a temporary solution. I always tell my clients that the most important thing you can do to stay at your desired weight is constant motivation. But you have to discover what motivates you. Everyone is different. For me, friends who are fit and mindful of what they eat is a great motivator. I also read about health to remind myself of what food does to my body (like the undesired affects of refined sugar). Once you discover the things that are motivating, you have to keep reminding yourself -daily-. Put up pictures on the fridge, on the wardrobe doors. Talk to like minded people daily. Watch shows, read books, buy some new clothes, etc.

If consuming less calories is too difficult, you can also try intermittent fasting. I find it easier to lose weight with i.f.

Of course you should first ask your doctor about this. Intermittent fasting is not suitable for everybody. Make sure you have no health condition that may harm you if you do i.f. But usually it is a safe thing for most people.

Good luck. 20 lbs is not that difficult, you can do it!

Omer