Hi geelouis, have you seen a doctor or physiotherapist about your back issues and have they prescribed any exercises for you? Curl ups, planks, and side planks are all quite demanding exercises for the low back and I would generally only suggest these to someone without back pain. Bird dogs, when done correctly, are excellent for building up some core stability and strength. It really is difficult to give suggestions online about exercise when there are injuries involved. To ensure someone is learning how to use their "core" it takes a lot of practice and feedback from seeing someone in person, which is where someone like a physiotherapist comes in. That being said, you can start with exercises that are easier on the low back, but will start to work on the ability to keep your core engaged while adding movement (and breathing!). Then, when you can do these exercises without pain, you can progress to more challenging ones, maybe eventually working up to things like planks.
Here are a couple of examples that I would normally begin with:
Deadbug
Lie flat on your back, with your lower back neutral (not completely flat against the floor and not overly arched). Place your fingers at your sides on the bony area of your pelvis just below your waist. Now tighten your stomach muscles as if you were about to get punched. Lift one foot a couple of inches off the ground while keeping your stomach tight and keeping your back in the neutral position. Then put your foot down and lift the other foot. Keep your hands on your pelvis to make sure that you are not tilting your pelvis as you lift your feet. Alternate the feet for 20 repetitions while keeping your pelvis stable.
Bridging
Lie flat on your back, bend your knees, and keep your feet flat on the floor. Find the neutral position as illustrated above. After which, lift your hips off the ground, maintaining a neutral position in the lower back and keeping the spine straight and your weight on your upper back. Lift your hips up until you begin to find it difficult to maintain the neutral position. Keep your arms at your side, palms down on the floor to provide stability so your hips do not tilt side to side. Lower to the floor and lift up 20 times. To increase the difficulty of this exercise, do alternate leg lifts while bridging.
Generally, I would only progress someone to a more difficult version of an exercise once they can do these a) while maintaining core engagement, b) maintaining a neutral spine, and c) they can breathe throughout the exercise. And I would strongly suggest seeing a professional in person.