So, here we are. I want so badly to stay married and keep our family together. However, I know I’ve betrayed my husband and caused so much pain that I can’t imagine him ever moving past my infidelity.
I guess my question to everyone is, (please, only helpful responses), how can I, is it possible, to show my husband: how remorseful I am and how much I love him and how sorry I am and how much I want to keep our family together.
I suppose this is nothing more than a selfish desire. But, I love him, I need him, our kids love/need him.
These are all good questions. And it seems that you are early in the process, so there is a lot of work to be done, and sadly, a lot of this work will involve a great deal of pain as you dig deep to find out who you really are, how you think and feel, and to learn to let go of the outcomes now.
Re-read the quote above. Even you said this is a selfish desire, but take that to heart. Notice that what you keep stating is what you want, how you want things to turn out, how you want him to feel... but how does this help your husband feel any safer about being with you? Does it show concern for him or what he wants and needs? I know that, as a WS, wanting your BS to stop hurting and to rebuild the marriage seems like the most loving and supportive thing you can do. But it is not. These words and feelings are all about you and your happiness, which means you are still putting yourself before the needs of your husband, the husband you just betrayed on so many levels.
While I cannot speak for your husband, I can tell you from my own experience that what he likely wants from you is to feel that you are putting him and his needs before your own, to feel that you truly understand how much damage you did, to show him true empathy, and to demonstrate to him, through your actions, not your words, that you are no longer an unsafe partner for him.
When you cheated on him, you showed him that in fact, you do NOT love him, do NOT need him, and did NOT think of him or the kids or anyone but yourself. Your words will feel meaningless to him because you said those words to him before and yet stabbed him in the back. Even if he was to believe that you are sincere and mean it, that you love him now and won't ever do this again, so what? Why should he care or love you back? To him, it probably feels as if you ran off and got to have your fun, while playing him for a sucker. As yourself, why should he love you now? Why should he trust you now? And why should he care what you want when you didn't consider his needs during the affair? You wanting him back simply may feel like you still making decisions for him, decisions that again benefit you and your needs, not his, not what may be best for him.
Please don't feel that I am beating on you. I am a WS too, just like everyone else on the WS forum, and we all did the same thoughtless and selfish things to our BS's. If there is to be any hope for reconciliation, then we need to get out of our heads and see how the thoughts and feelings we have, even when they seem loving and true to us, can actually still be very selfish and unempathetic. At 18 months out myself, and while still working as hard as possible on myself, I still slip into these thought patterns. It takes time and effort to recognize the broken coping skills we have as WS's, and to build new ways of thinking and feeling that are more healthy, for ourselves and for our spouses and families.
For now, please know that the best way to help your husband feel safer about you is to show him that he comes first in your world, in everything, even to your own detriment perhaps. Let me try to give you an example to think about.
Let's say that you contract a disease which you can survive, but that could be fatal to your kids if they caught it. As long as you have this disease, you are a danger to your children. What would you do about this? I'm sure you love your kids and would sacrifice anything for their safety. In this case, it might mean that you have to send them away to live with a relative, or move out yourself and let them stay with Dad. This would rip your heart out of course. It would be hard on you, hard on the kids and your spouse, and not what anyone wants. But wouldn't you do it because it is what is best for your kids? That is what sacrificial love is like. Now apply that to your spouse. He will have to do whatever he needs to right now to feel safe from getting hurt by you again. Do you support him in this? If so, that means putting his needs first. When he tells what he needs to feel safe, you need to make those things a priority in your life, even if it is not what you want.
You cannot do his healing for him. Like anyone after a trauma, he needs to go through the process of feeling hurt and sad, to grieve, to figure out how he feels and what he needs now that his world has changed, how to survive in a world where the person he trusted the most to have his back, stabbed him in the back instead In the same way, he cannot do your healing for you. You need to figure out why you allowed yourself to compromise your values and his safety. Why did you give yourself permission to lie to him, to your kids? What did the affair give you that you felt was missing? Figure out how you came to this point in your life where you became a liar and cheater, and who do you want to be moving forward? How are you going to get there?
This will be hard. And you need to accept the fact that, even if you became the world's most perfect person now, that it might not make a difference. If you truly put him first, then you may need to accept that his needs might not match your own. However, there are lots of couples here on SI who have been in successful R for years and years. Many of them report that their relationships are in many ways, better. More honest. More authentic. More supportive and understanding. You need to fix yourself, either way, R or D. Learn to love yourself, learn to be proud of who you are, get back to being someone you can respect.
You came to a good place. People here will be honest with you. The rest is up to you.