I'm going to try to keep this as simple as possible!
Our legs work in a closed chain environment (body part moves to the object/ground not object to the body part) whether you're playing sports, walking, running etc... Your legs are relative to the ground and gravity and work in chains with other muscles. Using leg machines does not integrate your core. Your core should absolutely be working with your legs. Isolating these muscles of the legs not only creates kinks in these chains but dumbs down your nervous system.
Squats:so many variations from single leg,split, front squat etc
romanian, russian, single leg,sumo etc
Lunges: all 3 planes of motion,saggital , lateral(great adductor exercise!) and tranversere plane, forward and reverse
Box Jumps, Jumping of all variations.
All of these exercises above can be performed at home or the gym and will train your hip extensors, flexors , abductors and adductors as well as integrating them with your core.
Now if you want to workout your abductors and do leg curls at home I would suggest you get the band and wrap it around your knees and do Supine Hip Extension With feet on Ball.. Two birds with one stone and this exercise will train your abductors like stabilizers and not prime movers. (tube walking is not beneficial because it's training your abductors like prime movers)
I hope this helps!