Since no one is really answering your question, I'll give it a go. First, anytime you are travelling by increasing the elevation, you exert more work on your body. Imagine this, lay out a path. One is two giant steps, almost like someone stacked two big boxes that you have to climb to get up 5 ft. Then for 50 ft you get to walk in a straight path. Now, instead of the initial two big boxes, you instead have to walk 50 ft with a steady incline. The whole time you are walking you will be exerting more work on your body with less recovery time. What you are experiencing is normal. Your body may need to do short bursts on trail B, but you get to recover on the flat areas for a larger portion of time. On trail A, it's like you are on a constant uphill climb with no way for your body to recover on a flat plane surface. Your leg muscles are constantly working to increase your elevation.
For your second point. For both, always stretch. It will keep you loose and drink lots of water, especially on trail A. For trail A, eat a long burning carb like oatmeal. It will help keep you going on the trail. Mentally you need to be prepared for the long haul. Keep a deep steady breath. Breath in through the nose and out through the mouth. Take breaks regularly and let your body rest if you are feeling too fatigued. But mentally, accept the fact that path A is just going to be more strenuous and that when you finish, you just accomplished a nice steady workout (helping your heart and endurance).
For path B since you are doing sharp increases in elevation, stretching is really important. You will be more prone to injury with quick thrusts on your muscles. About 30 min before a quick change in elevation, eat an apple/banana to give you some quick energy for that sharp increase that will burn fast. After you do the sharp climb, take a small break (2 min) and stretch. Then proceed on the level areas at a steady pace to keep your muscles warm.
When you get done with both, stretch again and take nice deep breaths. Drink plenty of fluids to avoid dehydration.
On a side note, if you want your hikes to feel more like relaxation instead of exercise, it's best to just get yourself in better shape. If you make sure your physical activity when you exercise is more strenuous than when you hike, hiking will be a much less demanding activity on you and will feel like a day in the park compared to your regular workout routine.