Thanks for responding.
LondonBoxer and humble have also written in and they should be considered subject matter experts with regards to training to get in the ring. I know that calling your friend/coach in the videos into some question may seem rough, but understand that 1;they are going off of a few clips, and 2; they are doing it with your interests at heart.
Now I am going to make a few suggestions, bearing in mind that I am not a SME with boxing or muay thai and that my advice is geared towards getting you into a "hits hard enough to hurt you"/martial arts/self defense context.
First, I want you to chase down a pdf copy of Jack Dempsey's Championship Fighting. It is a 1950 or so publication and I think falls outside current copyright law, so you aren't doing anything wrong by going the download route. A quick google search should get you there. Read the whole thing, but I really want you focusing on the jab/jolt and "drop step/falling step" material first. DO THIS AS SOON AS POSSIBLE. Like as soon as you read this. This will give you some inroad into the "hitting with power" part of the equation.
Second, I think you need some work on balance, moving with balance, and being ready to hit from a position of balance. Read humble and LondonBoxer's posts and let it sink in how much of a priority developing this is.
Now, I don't know where you are at with regards to finding a fighting gym, commitment to your current gym/trainer, and time. I will echo the notion that 1 x a week and irregular at that is not going to buy much in terms of improvement, at least past a very early point. To this end I am going to recommend you start doing some focused training at home.
The following is a suggestion for that work.
DISCLOSURE: This is not to take the place of in gym training. It is a supplement to real instruction. Additionally, I am not a boxing or muay thai coach. If any of the advice below is disagreed with/advised against by either of the SME's also posting in this thread you should consider their opinions to havae "veto" power over mine. Also, it is early and I am not properly coffee'd up. So deal with any typo's and grammar errors.
The following work is to be done every day you are not formally training. So if you are not seeing your coach, you work this. Additionally, you are to "walk through" the material/techniques your coach has you work in the formal class at least once before the next class. This is my standard advice for any martial art/skill and makes a difference all on its own.
A.) Balance Awareness work- In your videos I am not sure you are ever in a really balanced position. If you come to a fight without a sense of balance, you are doing your enemies work for him.
If you are familiar with the Tree pose from yoga then that will help. If not, you are about to get really familiar.
I recommend doing this without shoes.
1.) Get in your fighting stance, hands up, chin tucked, ready to fire either hand. Bend your knees/sink slightly and "feel" the ground with your feet and "feel" where your "center of balance is". Gently shift your weight forward, i.e. bend your front leg a bit more and feel that. Shift back and feel how that goes. You should be breathing through your nose and SMELLING the air. IF you can smell, you are breathing slow and calm enough.
2.) Draw up either leg and go into the Tree pose. Watch this video and mimic. Do only one side. When you lose your balance or feel you are done, step down.
3.) Go back into your fighting stance. Repeating Step 1. FEEL your hips, the ground, everything.
4.) Go into Tree pose for the opposite side/leg. When done start again at 1.
So it goes Stance-Tree-Stance-Tree(other side). Repeat this for 5-6 minutes of honest work(2 rounds, but don't wed yourself to the timer). Doing it barefoot, and outside(if you have a nice view/fresh air) can be enjoyable. But just do it even if you have to do it inside.
B.)Balance in movement- You are going to need a bit of space. Outside or in doesn't matter as much here. The space you have will somewhat decide how "big" or "small" this drill gets. You are going to be tracing a square, and I would like you to be able to take 2 or 3 steps for each "side" at least.
Get in your fighting stance, balanced, and ready to fire either hand. The direction you are facing is the "number 1 wall", and will be faced at all times. Think of it as a wall/direction and don't focus at a spot. To move, you are going to step with the foot that is closest to the spot you want to move to. So front foot first for fwd, back foot for back, left for left, right for right. Then slide the other foot into position. Begin with forward. After each step, you should be back in your balanced, ready to punch, stance. Don't rush. Every step just moved your position. Take these measured steps forward. Take your time.
When you run out of forward room, start stepping right. Continue to face the same direction as you did when stepping forward, so now you are side stepping. Fight the urge to "square up" to the "number 1 wall". If you are doing this in front of mirrored wall, you would always look directly at your reflection. You don't need a mirrored wall. In fact, I don't want you to use one. I want you to feel yourself in space. NOT need to see yourself.
3.) When you run out of real estate again start stepping back.
4.) When out of room start stepping left. You should end up back where you started.
Do this for 3 minutes/1 round.
C.) Power generation/weight transfer- We are going to begin with the jab, as per LondonBoxer's advice. This means we are going to be working the "drop step"/"falling step" that Dempsey wrote about. Follow his advice in the book for 3 rounds. At first you will just be practicing the step/power generation without hitting. Then you are going to work into throwing and landing your jab/jolt on the heavy bag. Use wraps and gloves for this. Work just the jab. Make it yours.
GENERAL: Wraps would interfere with the exercise in A. They are inconsequential for B. You will want wraps and/or gloves for C. If you are doing A and B outside than wait to wrap your hands until you go inside to your heavy bag. Don't be the guy that has to wrap his hands and put on boxing shorts to do road work.
Hopefully the above was helpful.
I need coffee.
I have to get to the office.