Bravo! I salute your creative genius when it comes to the way you dealt with Sesshoumaru's manner of speech. Everyone passes off him saying "This Sesshoumaru" as being a formal way of speaking, but you gave us another very reasonable option for that: a separation of Sesshoumaru and his "inner youkai." I really like that. Nice work!

I really love the uniqueness of Kagome going to Kouga for help when she decided to leave Inuyasha!

What? Did Shippo just ask to court Rin!? Wait... How old is Rin?

Inuyasha turns human on the night of a new-moon, not a full moon.

Porfavor continúa con la historia está buenísima

Im just going to read everything and write down all my thoughts and send it all in a PM at the end... the story is a good one, it could just use some touch ups and a bit more research so far and a few plot holes filled up that I spotted so far.

Also, a lieutenant and a general are too high up in the ranks to train rookies. You usually have Sergeants running around with the rookies. (There are different types of Sergeants)

snap to attention if necessary. You will also be ordered on what you should wear that day depending on the training. If there is any type of training in the pool females must wear conservative one piece suits. “You are there to train, not to show off your skin”. Usually you will have to carry around what is called a “camel pack” which is a thin bag that goes on your back similar to a back pack but carries a certain amount of water. You drink from a rubber tube that has a square shaped nipple on the end and a lid to go over the nipple. Usually when training the formation might get the order to “DRINK WATER!” This happens pretty often. There is usually always an area for you to refill your camel pack.

Also, Koga is a male. Therefore he would be Nii-san, not Nee-san. The i is for males and the e is for females. If you decide to use Iie instead of no, it is not Lie but iie. Which to us English speakers is pronounced “Eee-ehh”.
Kirara is the name of the fire cat, not Kilala. I can’t currently use hirigana on this keyboard but it’s easy enough to go by sound ki-ra-ra. There is no “La”. My Japanese language knowledge is pretty limited because I haven’t touched it in a long while though.
I like your story, this is just me giving you more information that might help you edit it to be better and maybe will help in future stories. Also, a previous commenter mentioned how you kept misspelling Hakaku (I think it was, I noticed, but didn’t really bring it up.)
To be honest, I expected Kagome to go to a Dojo to train more. There are thousands of fighting styles and weapons she could be able to learn to use, even for the feudal era.

Barracks separate male and female subordinates into separate buildings. The rooms are filled with many bunks made from metal frames with a drawer directly beneath each mattress. Bottom bunks are coveted because of how narrow the beds are and because it is easier to get up quickly and make the bed before it is inspected by a superior. Along the walls are metal lockers that have shelves within as well as drawers. You are expected to bring your own locks and keep them organized. Each morning you must get up and get dressed and fix your bed as quickly as possible. The showers and toilets are usually in the same floor and there isn’t a door, you just turn a corner and the toilet stalls are there, turn another corner and there is a room filled with shower heads where you must shower with everyone else. After inspection everyone must go stand outside in formation. After formation everyone marches to breakfast and then back to formation before training begins. Each night, there is a list of people to sign up for fire watch. Every hour is a different person. The person whose shift ends must go and wake the next one before going to bed. Everyone is usually in bed by 10 pm. Depending on what you do that day and the schedule you may only get 2 or 3 hours of sleep before waking up early for training. It is encouraged to have some sort of food on you at all times but you are not allowed to eat unless you are ordered “At Ease” in formation which is where you can move around some but your foot (left I think, might be right, it’s been a while) must remain in the same position so that you can snap to attention if necessary. You will also be ordered on what you should wear that day depending on the training. If there is any type of training in the pool females must wear conservative one piece suits. “You are there to train, not to show off your skin”. Usually you will have to carry around what is called a “camel pack” which is a thin bag that goes on your back similar to a back pack but carries a certain amount of water. You drink from a rubber tube that has a square shaped nipple on the end and a lid to go over the nipple. Usually when training the formation might get the order to “DRINK WATER!” This happens pretty often. There is usually always an area for you to refill your camel pack.

Also, Koga is a male. Therefore he would be Nii-san, not Nee-san. The i is for males and the e is for females. If you decide to use Iie instead of no, it is not Lie but iie. Which to us English speakers is pronounced “Eee-ehh”.
Kirara is the name of the fire cat, not Kilala. I can’t currently use hirigana on this keyboard but it’s easy enough to go by sound ki-ra-ra. There is no “La”. My Japanese language knowledge is pretty limited because I haven’t touched it in a long while though.
I like your story, this is just me giving you more information that might help you edit it to be better and maybe will help in future stories. Also, a previous commenter mentioned how you kept misspelling Hakaku (I think it was, I noticed, but didn’t really bring it up.)
To be honest, I expected Kagome to go to a Dojo to train more. There are thousands of fighting styles and weapons she could be able to learn to use, even for the feudal era.

Eh... signing up for the military isn’t that simple... you have to go to a recruiters office. They will have you do a physical exam where they make sure you are healthy enough and there are height and weight requirements. After that, you have to make sure that they have all of your personal information like social security card number and ID and birth certificate and a couple of other things. You also have to take what is called an ASVAB which is a test that measures your knowledge in every area from Science to English to mechanics as well as be able to run 2 miles within a certain time as well as do push ups and sit-ups (a certain number within 2 minutes) once all of that is done they take your results and try to work with you to find the best position for you. Of course, this is only relevant to America. Japan no longer has a military. They were banned from having one by the UN for their attack on peal harbor. Also, IF they had a military, it would most likely have similar tests and would take a few months to be processed before they were shipped off to basic training where they push you past your limits as well as teach you everything you need to know for your job and EVERYONE has to go through a gas chamber without a mask. I haven’t done any of this personally but I have a lot of military family and spent most of high school in the Junior Reserve Officer Training Corps and actually went to train in Ft. Jackson in Georgia and lived with my sister for about a year in Ft. Bragg North Carolina as well as Joint Base Lewis McChord (which is both Army and Air Force I think) in Washington State.

44B? Kagome is pretty thin and she’s Japanese. 44 is the inches around the waist. Plus she’s around what, 15? I’d say she’s probably more like a 34B realistically, maybe even 32...

Ah, you keep spelling names wrong... maybe you should get a beta?

As a Demon Slayer, wouldn't Sango know more about yokai custom than others?

Hmm interesting to read

Incomplete:/