"What can we do on this point to finally attain communion?"

Erm... enter into communion, maybe?
I do not understand such questions, or rather, I do not understand the asking of such questions as this-

I’m [a Lutheran married to] a Roman Catholic Christian. We have been living happily together for many years, sharing joys and sorrows. And, therefore, it’s quite painful to be divided in the faith and to be unable to take part together in the Lord’s Supper. What can we do on this point to finally attain communion?

I do not understand the asking, when there is a clear answer, one that no one has ever hidden, that is widely proclaimed, broadly advertised: come into full communion with the Church, profess what the Church teaches, become a member of the Church.

If you believe what the Church teaches you know this and there should be no problem.
If you don't believe what the Church teaches you know this and you already know what the problem is.
If the Church is Who She says She is, you should be beating down the doors to be a member. If She isn't why would you want in?

And strangely, the gentleman to whom you addressed the question, the Successor of Peter? is himself actually part of the answer, from what I know of Lutheranism.
As I say, I think I understand the question.
But as usual, I don't really understand the answer given.

It’s not easy for me to respond to your question about sharing in the Lord’s Supper. especially in the presence of a theologian such as Cardinal Kasper. I’m afraid!

I think the Lord has said it to us, when He gave this mandate: “Do this in memory of me.” And when we share the Lord’s Supper, we recall and imitate, we do the same thing that the Lord Jesus did. And there will be the Lord’s Supper, there will be the last banquet in the New Jerusalem, but it will be the last.

Instead on the journey, I wonder – and I don’t know how to answer, but I make your question my own,  -- I wonder: is the sharing of the Lord’s Supper the end of a journey or the viaticum to journey together? I leave the question to the theologians, to those who understand.

It’s true that in a certain sense to share is to say that there are no differences between us, that we have the same doctrine – I stress the word, a word that is difficult to understand – but I wonder: don’t we have the same Baptism? And if we have the same Baptism, we must walk together.

You are also a testimony of a profound journey, because it’s a conjugal journey, in fact, a family journey, of human love and shared faith. We have the same Baptism. When you feel yourself a sinner – I also feel myself very much a sinner – when your husband feels himself a sinner, you go before the Lord and ask for forgiveness; your husband does the same and goes to the priest and asks for absolution. They are remedies to keep Baptism alive. When you pray together, that Baptism grows, it becomes strong; when you teach your children who Jesus is, why Jesus came, what Jesus did for us, do the same, be it in Lutheran language or in Catholic language, but it’s the same.

The question: and the Supper? There are questions to which only if one is sincere with oneself and with the few theological “lights” that I have, the same must be answered, you see to it. “This is my Body, this is my Blood,” said the Lord, “do this in memory of me,” and this is a viaticum that helps us to walk.

I had a great friendship with an Episcopalian Bishop, 48, married, with two children, and he had this anxiety: his wife was Catholic, his children were Catholics, he was a Bishop. On Sundays he accompanied his wife and his children to Mass and then he went to worship with his community. It was a step of participation in the Lord’s Supper. Then he went on, the Lord called him, a righteous man.

I answer your question only with a question: what can I do with my husband so that the Lord’s Supper accompanies me on my way? It’s a problem to which each one must respond. But a friend who was a Pastor said to me: “We believe that the Lord is present there. He is present. You believe that the Lord is present. And what is the difference?” Alas, they are explanations, interpretations ...” Life is greater than explanations and interpretations. Always make reference to Baptism: “One faith, one Baptism, one Lord,” so Paul says to us, and from there take the consequences. I would never dare to give permission to do this because it’s not my competence. One Baptism, one Lord, one faith. Speak with the Lord and go ahead. I don’t dare say more.

He doesn't dare say more.