Is it considered disobedience (عقوق) not to house one's parents in the marital home, provided a separate, nearby apartment is rented for them and they are cared for? And does the Almighty’s saying, "And if either or both of them reach old age [while] with you," imply an obligation to house them in the same home? What is the ruling if the excuse of a small house is no longer valid?

You are not obliged to house your parents in your home, and this is not a shortcoming in filial piety. Rather, the obligation is to financially support them if they are in need, to serve them, to maintain ties with them, to check on their well-being, and to obey them in what is good. The verse: "And your Lord has decreed that you shall not worship except Him, and to parents, goodness. Whether one or both of them reach old age [while] with you, say not to them [even] 'uff,' and do not repel them but speak to them a noble word" does not command housing parents in the marital home. Instead, it commands righteousness, care, and kindness towards them, whether they are with you or in another home. The meaning of "with you" (عِندَكَ) is that they should be under your care and responsibility.