Firstly, I wanted to express that transexual is generally considered a misnomer from transgender. However, what you describe does sound somewhat congruent to what this actually has... So then I ask for some elaboration.
Are you experiencing dysphoria, or are you experiencing dysmorphia, or are you experiencing dysphoria AND dysmorphia? Do you believe that to be a woman, you have to meet the condition of having or wanting female genitals?
If you are transgender, then you experience dysphoria because people assert that properties about you are not what aligns with your internal identity and self. If you are transsexual, as in the real definition of transsexual, then you have dysmorphia over not being born a female.
Being male or female, or having a certain genital set, isn't related to your self-expression though. You are trying to tie your personal identity of woman to your body, but it isn't about your body it is about your social presentation and self.

And to be clear, this assumes that you are misnaming transgenderism as transexualism.

It is understandably confusing; you are used to seeing the things that you like, and the way you want to look associated with females. The same reason transgender women have gender-affirming care to make them more easily present as if they are females. If it is the case that you are actually transsexual, your goal is to become a female -- not a woman.. This is not the same as being transgender.

I understand 100-percent why it might be too much, and you might want to detransition or stop your transition -- or what have you. From my experience, and I suggest deep down inside yourself you know this, that isn't going to work. If you feel that the identity of woman better describes what you are, then you are best categorized as a woman -- you would no, not anyone else. Being a woman is not conditional to looking like a woman. If you are a woman, you've been a woman your entire life. I'm sorry sister, but you're not a man. This is the case whether you ever externalized your identity or not.

I think your children are a very interesting observation. There are more ways that someone can be strong than physical. You are their parent, their love for you and the way you are is not going to be conditional on what you are, but who you are. Your children don't lose anything by you being transgender, you are still there. And if anything, you are happier.

What if one of your children were to be transgender, or different in another way, and your courage gave them the courage to stand as themselves?
The notion that children " need a mom and a dad" is verifyably false, as it has been proven that same-sex couples tend to raise children BETTER than heterosexual couples. Might be partially attributed to them being able to make a lot less errors, but the point is your children can survive just fine whether you are presenting as a man or a woman. What really matters is that you are there. If your wife is okay with you being transgender, and she supports you and wants to be with you despite this, then you are keeping the family together: the biggest thing, something that matters.

Of course there's also the concern of ridicule and all of that, but if your kid got made fun of because you are a Muslim, would you stop being a Muslim. You can think of gender as something very similar to religion; like religion, it is not tangible and it is socially constructed. Also like religion, gender is personal.
I don't think that social pressure should make you change your religious identity, so why should social pressure make you change your gender identity?

I'm not going to try and convince you that this is what you need, I don't know you or what you need. I also understand what this life is like, and live in Alabama, so I completely understand not wanting to do it anymore. Especially when you experience the sharp difference in how you are treated, and how different people in your life react to this change.

Just know you weren't born with a burden; society has placed a burdon on you. You are blaming your birth for sex homogeneity that has been forced for thousands of years pretty much exclusively to oppress women. It's almost hilarious to think about this in the frame of social standards...
- women are meant to listen to men, who are the controllers of the relationship.
- if a woman is fat, she is gross, if man is fat he is just fat.
- despite growing leg hair, somehow not having leg hair is intrinsic to being a female.
All of those are components of an identity, and a role. I get the inclination that you might be uncomfortable with your own body because it has been drilled into your head that someone with your body cannot be who you are, but that's so clearly not the case because you are who you are and you have your body.

The normal cycle for a transgender woman's entire life is pretending to be a man for as long as possible before exploding over a short period of time, often returning back to pretending after. Usually there is some negative emotion associated that brings someone back, too. Eventually, they might end up undergoing a transition. In the cases where they don't, they eventually do -- only now they haven't lived their life, but a life someone else defined for them -- and they wasted all of their time living their life in a way which was not genuine. You only have one life. I know it's hard, but is there really any other option?

I believe in you. If you have Twitter, feel free to reach out if you ever need anything; the link is in my Medium profile. Also I want to note that a lot of this comes from my personal experiences. I am not every transgender woman, and I can't sit here and say that the benefits of being yourself outweigh the negatives. I'm also a bit different, as I am XXY intersex and AMAB, and I am sure that in some ways male transgender people's experience could differ from mine, so keep all of that in mind.
Also, this reaching out is not conditional on what you decide to do, girl. Do what you want to do and if you need support in that then don't hesitate!
I love you 💜 stay safe and take care of yourself.