For those that are not aware, Dollyo Chagi is a roundhouse kick, and Yop Chagi is a side kick.
Flexibility is key for Tae Kwon Do (TKD), as the style heavily favors kicking, and especially for World Taekwondo Federation type sparring (Olympics) it is the major scoring technique. Very little scoring in WTF is done with hand techniques.
From the description that you give, it sounds like you have very tight hamstrings, which is not that uncommon. I went through several links on google and this page has what I would consider the best 4 hamstring stretches.
When I stretch, I go through a progression, designed to hit all the major lower body muscle groups which I outline below. I generally do this directly after class or form work. Hold each stretch for 15-20 seconds, then relax, exhale and reach/hold for 15-20 again. Generally I get a little further on the second stretch than the first.
Once you get more advanced, you can look into something called Proprioceptive Neuromuscular Facilitation (PNF) which can get somewhat extreme and is only recommended once or twice a week. Also, you can look at Bill Wallace's book "Dynamic Stretching and Kicking". While somewhat dated, all of the basic stretches are there and you can develop your own routine. Just make sure that you modify it for modern understanding of safety (Such as the hurdler stretch, place your foot next to thigh, not out to side and behind).
The stretches that I do are as follows (I generally stretch hamstrings, then inner/groin, quads then calves/feet, although my order and stretches may vary.) I don't do much partner stretching, as I've had overzealous partners do some damage before.
- Standing hamstring - Feet together, your standard "hang and reach". Try to keep your back more flat, not rounded. Don't push this too hard, as there is some risk to the lower back.
- Straddle stretch - Think Annon Chagi (Horse/Middle stance) but with mostly straight legs. Reach to floor. I do one set with feet shoulder width, and then one set with a fairly wide foot base.
- Quad stretch - Pick foot up behind you, try to touch it to your butt. Advanced - Arch backwards at same time.
- Hurdler stretch - Foot tucked into thigh
- Front splits - As far as I can go, not quite to full yet.
- Rotational - This link shows it, hard to describe
- Butt - Lay on back with feet like you were sitting cross legged (one foot on opposite knee) - Reach under crossed foot, pull lower leg into body, which will stretch the crossed leg. Repeat on other leg.
- Straddle - Sit on the floor in a straight leg annon chagi type position (Stretch #2 but seated) and reach to right, left, center.
- Calves - Your basic pike position (Pushup position with a bent middle instead of straight), "walk" your hands forward until your heels just start to lift off floor.
- Sitting on toes, then sitting on tops of feet will work the fascia and muscles in the feet.
With anything, monitor. Stretches should be a little uncomfortable, but should never hurt. Never "push through" pain on a stretch. If it hurts, you're either doing it wrong or you are stretching too far for your capability. Also, never stretch without some kind of an active warmup first. Stretching on "cold" muscles is a good way to hurt things. Read through basic yoga, figure out what you like and works for you. These two links from the martial arts stack exchange site are also good:
Flexibility for karate kicks
Flexibility for round kicks
As far as control, that just takes lots and lots of practice. Grab a bar or other support, and work on slow, controlled kicks. When we teach, we do a four count of chamber, extend kick, rechamber, return to start position. Hold it in various spots. Good kicking is a combination of relaxation until just before impact, muscular strength, flexibility and lots of repetitions.
For example, on your yop chagi, if your hip abductors (The muscles responsible for raising your leg to the side) are weak, you won't be able to raise your leg as high, and if you are inflexible, then you are fighting that. It all works together.