Nachmanides on Kiddushin 10, regarding intercourse with a Canaanite maidservant, wrote that intercourse done in a prohibited way does not effect acquisition.

"Just as with a Canaanite maidservant, whose intercourse does not entitle her to eat terumah, etc.—this is difficult for me: what comparison is there? There, the intercourse is prohibited, and since she is absolutely forbidden, how could it acquire…"

Maybe this can be explained as meaning that prohibited intercourse does not indicate ownership.

As for the question itself, the Ritva asks this on 10a and answers that intercourse for the purpose of marriage is permitted, even in her father's house.

As for Nachmanides, the intercourse is prohibited there for the same reason that it does not acquire: because there is no betrothal with a Canaanite maidservant (just as with a gentile woman). You can't learn from there that prohibited intercourse does not acquire, and certainly not intercourse that is prohibited only rabbinically.
As for the Ritva, his words seem astonishing to me. As I explained, there is no difficulty here. Maybe he understood that it is entirely permitted to have relations in her father's house, but I don't understand why one should read it that way.
And after I wrote this, I remembered the famous story about Rabbi Chaim Brisker (“there is no such Tosafot”), and I said to myself that there probably is no such Ritva either. And indeed I looked in the Ritva there and saw that he does not write this:

And our master, the Gaon Alfasi of blessed memory, answered that here it is speaking of intercourse without prior betrothal, whereas there in Yevamot it is intercourse after betrothal by money or document; for once he had intercourse with her after betrothing her, even though she had not entered the bridal canopy, he acquires her as his full wife regarding inheriting from her and becoming impure for her. This too is precise from the fact that we say there: from where do we know a woman for her husband? And this is what we derive by the gezerah shavah of “taking” “taking” from the field of Ephron—meaning that where there is “he takes” and “he has relations with her,” namely intercourse plus betrothal, he acquires her. But this does not seem right, for nowhere do we find that intercourse after betrothal by money without a bridal canopy acquires, for on the contrary, such intercourse is prohibited, and one who has relations with his betrothed in her father's house is flogged; and so too it is proven in Yevamot that intercourse after betrothal without a bridal canopy is mere promiscuity. Rather, one may say that there it speaks of one who has intercourse without specifying intent, but if he has intercourse for the purpose of marriage after betrothal, then he thereby effects marriage. So too Maimonides wrote.

What he writes is that if the intercourse is done for the purpose of marriage, it effects marriage and is not promiscuity. He does not write that there is no prohibition here (rabbinic, against having relations with one's wife in her father's house. There is no prohibition of promiscuity, because this truly is not promiscuous intercourse).

Does the Rabbi understand that when the Ritva says, "there it speaks of one who has intercourse without specifying intent," that refers only to the Gemara in Yevamot and not to the words of Maimonides?
A. As a matter of logic, I don't understand: if this intercourse effects marriage, why should he be flogged—what is wrong with this intercourse?
B. Nachmanides there says: "But I do not know that intercourse without a bridal canopy should acquire for inheritance and the other matters of marriage, for such intercourse is prohibited and resembles promiscuity—so how could it acquire? And this too is proven, for in 'Ha-Achin' 29b it does not acquire. But his student, Rabbi Moshe, of blessed memory, says that one who has relations with his betrothed for the purpose of marriage—that is her bridal canopy. So you find that intercourse acquires for the purpose of marriage, and the bridal canopy acquires for the purpose of marriage; but one who has relations with his betrothed in her father's house not for the purpose of marriage does not acquire and is flogged by rabbinic decree."
Here it seems clear that one who has relations with his betrothed in her father's house for the purpose of marriage is not flogged, as I explained in the Ritva. And in the Ritva too, it seems to me that this is the explanation, because he wrote "and so too Maimonides wrote," and this is the Maimonides that Nachmanides cites.
C. It seems to me that from the above Nachmanides we see that prohibited intercourse does not acquire, regardless of the nature of the acquisition.

A. As stated, there is a rabbinic prohibition. We are talking about disciplinary lashes, not a Torah prohibition. They also forbade ordinary betrothal through intercourse (because of the one who acted brazenly with his wife under the tree), but I don't think anyone disagrees that if he did so, the intercourse effects acquisition.
B. Here too, the inference is not necessary. It could be that one who comes for the purpose of marriage is flogged and still acquires.
C. There his intent is not clear to me. Maybe the fact that there is a prohibition is because it is clear that his intent is not to acquire but for promiscuity. And it is also possible that we're really talking about prohibitions of that sort, which involve promiscuity, and not every prohibition (as with ordinary betrothal through intercourse, where I don't know of anyone who says it does not acquire because there is a rabbinic prohibition). Or perhaps he is innovating that there is a disqualification here like a commandment fulfilled through a transgression? That seems forced to me (first of all because this is not a commandment, and besides). In short, I see no reason why the prohibition involved in the intercourse should prevent the legal effect of betrothal or marriage.

My initial understanding was that the Sages forbade a groom from having relations with his betrothed before the stage of marriage has been completed (because it has an element of licentiousness). "One who has relations with his betrothed in her father's house" is just a common example of intercourse not for the purpose of marriage (because an ordinary person doesn't usually have explicit intentions at the time he has relations with his betrothed; rather, the surrounding circumstances reveal his general intent—if they made a bridal canopy and feast, that's a sign that the groom intends marriage, and if they didn't, and the betrothed woman is still in her father's house, that's a sign that he does not intend marriage). From this I concluded that even if the intercourse literally took place in her father's house, but for the purpose of marriage, there is no problem here. For example, nowadays it is common for the bride and groom to live in the parents' home of one of the spouses. In such a case it seems there is no problem.

I went halfway with you. The prohibition indicates that there is no such intention. And maybe that itself was the reason for the prohibition. But once it was prohibited, it is prohibited. Still, there is not necessarily any connection to the concept of marriage itself. Meaning, if he intends to marry her, it will take effect despite the severity of the prohibition.
As for the reasoning itself, it seems simple to me that "her father's house" is not a geographic location but means as long as the woman is under her father's authority and not yet married to him. So when they rent as a couple in her parents' home, that is also his home and not her father's house.