Is there a single word to express someone feeling lonely in a relationship with his/ her partner?

The commonly used phrase that suits such a description is unrequited feelings/love.

Where unrequited, as defined by AHD, means—

Not given, rewarded, or felt in return: unrequited love

Thus, you could say— Loneliness is a bad thing, but unrequited feelings/love is even worse.

EDIT— The OP has significantly modified the question, which now calls for altogether a different word or expression. Going through the rephrased version of the question, I suggest a wrong relationship ,which fits the bill nicely.

Alienation, is appropriate but there usually needs to be context or a qualifier. As in Italian and Hungarian, I don't think that there is a single English word for this.

OED: alienation, Also with from, n.

1.a. Estrangement; the state of being estranged or alienated.

1966 J. Cheever Jrnls. (1991) 216 He explained that I had developed a social veneer—an illusion of friendship—that was meant to conceal my basic hostility and alienation.

1971 B. Sidran Black Talk v. 152 This alienation from mainstream culture, then, remains basically a circular and unresolvable problem peculiar to the Negro.

2004 N.Y. Times (National ed.) 4 Jan. ii. 32/2 Punk is a vast support group for misfits, a community united by alienation.

MW

alienation noun

1 : a withdrawing or separation of a person or a person's affections from an object or position of former attachment

Alienation … from the values of one's society and family— S. L. Halleck

Study Sociology

Alienation is defined by the text as: The condition in which the individual is isolated and divorced from his or her society, work or sense of self.

I found more than one song called: Lonely Together.

However, I would say:

Loneliness is bad but feeling lonely in two is worse.

or

Loneliness is bad but loneliness in two is worse.

Sometimes such repetitive sentences "catch" and sound more powerful than if you try to explain too much.

Note: you may want to add a comma before but.

The single word that you are looking for might as well be loneliness itself as it doesn't apply only to a context of seclusion. However a term that might be more apt in your case is "emotional isolation". The phrase can then be: "Loneliness is bad but emotional isolation (in a couple) is worse." It is neither much shorter nor necessarily better than the original one.

Loneliness is already perfect. I'd say you have used the specific word for the general case. You should rather replace the word in the first part. If it has to be a substantive, you can say: "Solitude is bad but loneliness is worse." or "Soleness is bad but loneliness is worse."

If you can be flexible with the structure of the sentence, "Being alone is bad, but being lonely is worse" sounds more natural to my ear. The message is subtle, but the distinction is there.

However, I'm not a native speaker.