The muscles in the lower body, including the hips, glutes and thighs, are the strongest muscles in the body and it can be difficult to fatigue those muscles simply because you're limited by how much weight the upper body can support. You can get around this with a leg press machine, a squat rack or a smith machine, but there are other alternatives if you're working out at home and can't safely hold the amount of weight your lower body needs to be challenged.
Adding power to your lower body workouts can add intensity to your routine as well a new dynamic, helping you increase your power and strength. Try adding a power move before each lower body exercise, for example power jacks before a set of squats or power lunges before static lunges. I find these types of power moves work well with more endurance-based exercise (e.g., 12 or more reps of each exercise), but experiment to find what works for you.
Power moves aren't for everyone, so if you have knee, hip or ankle problems, you may want to skip the jumps and keep things low impact. The key with power moves is to land with soft joints so that your muscles take the impact, not your joints. Pay attention to how you feel during your workout and back off of the power moves if you feel your energy is waning, especially if you're using heavy weights. Form can slip as you get tired and power moves can magnify that fatigue.
Begin with feet together and jump up, taking feet out to the side, landing in a low squat. Jump up and bring feet back together (a very slow, powerful jumping jack). Swing your arms overhead to add intensity, repeating for 30-60 seconds.
Begin in a lunge position, right foot forward, left foot back, both knees at 90 degree angles. Jump up and switch feet in the air, landing in a lunge with left foot forward, right foot back. Make sure you land with soft knees to protect the joints. Repeat for 30-60 seconds.
Stand with feet wide, a kettlebell or weight in the right hand. Pivot and turn the body to the right and lower into a lunge. As you push back up, swing the weight up and over the head as you pivot back to the front. Switch hands and pivot to the left, lowering into a lunge and taking the weight down beside the lunging knee. Continue alternating sides while swinging the weight up and over (if you're advanced, you can toss the weight to the other hand at the top of the motion) for 1-3 sets of 10-16 reps (1 rep includes lunging to the right and left).