Two luxury real-estate projects in Albania proposed by the son-in-law of former President Donald J. Trump are stirring up lingering tensions in that country, with the Trump family facing accusations that land it hopes to develop has been improperly set aside for them.

The disputes relate to $1 billion worth of investments that Ivanka Trump, the former president’s oldest daughter, and her husband, Jared Kushner, are pursuing in Albania along the Mediterranean coast of this Southern European nation on land once controlled by a Communist government.

Mr. Kushner announced plans to build an opulent hotel and beach villa complex on a stretch of the mainland where an Albanian family has farmed for generations. The family says part of this property was corruptly seized from them after the end of Communist rule in 1991.

“They are trying to take from us what is ours,” said Bledar Alexandros Konomi, who as a young boy used to help tend cattle on the land now proposed for Mr. Kushner’s hotel and whose claim is backed up by Albanian court records.

At the second site — a small, strategically located island called Sazan where the Soviet Union sent military supplies during the Cold War — Mr. Kushner is working with top government officials in Albania to secure exclusive development rights.

What has not been public is that there is a second proposal to redevelop the same island submitted by an Albanian American real-estate executive developer from New York, according to documents obtained by The New York Times.