Not only were their "two" tabernacles in David's time, there were almost certainly more than two. Tabernacle (מִשְׁכָּן) is a fancy English word for "tent" or dwelling place. KJV uses it in the sense of "tent" in Num. 24:5
How goodly are thy tents, O Jacob, and thy tabernacles, O Israel!
Thus any covered Israelite sacred shine was a "tabernacle." However in the view of later biblical writers there could be only one official tabernacle at a time. This attitude, however, is anachronistic.
The Bible states that the tabernacle had been at Shiloh where it remained for most the period of Judges. Shiloh thus became a place of pilgrimage for Israelites who wished to offer their tithes and sacrifices there. However, local altars were also allowed at such sacred sites such as the high places of Gilgal (1 Samuel 11:14), Bethel (Judges 21:2), Mizpah (Judges 21:5) and—according to Samaritan tradition-—Mount Gerizim (Deuteronomy 27:11-13). Each of these is mentioned as an apparently legitimate worship site in the biblical text. While we have no concrete evidence that these altars were housed in tents, there is no reason to doubt that some of them were.
During David's early life, Samuel regularly visited the Israelite shrines at Bethel, Gilgal, and Mizpah. "He judged Israel in all these places." (1 Samuel 7:16) Thus the presence of the official Tabernacle at Gibeon does not mean that other Israelite tabernacles did not exist elsewhere.
The Books of Kings speaks of the high places as centers of apparently legitimate Israel worship a generation after David moved the Ark of the Covenant to Jerusalem, until the Temple was built:
The people were sacrificing at the high places, however, because no
house had yet been built for the name of the Lord. Solomon loved the
Lord, walking in the statutes of David his father; only, he sacrificed
and burnt incense at the high places. And the king went to Gibeon to
sacrifice there, for that was the great high place; Solomon used to
offer a thousand burnt offerings upon that altar. (1 Kings 3:2-4)
Bethel too apparently remained active and was not deemed illegitimate until the rebellion of Jeroboam I which the prophet Ahijah initially sanctioned.(1 Kings 11)
To conclude: In hindsight, we can distinguish between the official Tabernacle and temporary or local tent-altars where sacrifices and sacred vows were also made. But there were certainly more than two local centers of Israelite worship in the time of David.