I would like to know if dancing of any kind was every a part of Jewish worship
Dancing was evidently very much a part of daily and religious life of ancient Israel.
The yearly festivals were celebrated with dancing by both men and women. According to the Talmud, "pious men and men of affairs" would celebrate the water drawing festival at the end of Sukkoth by dancing with torches in their hands.
We are also told that on the 15th of Av and Yom Kippur, the women of Israel used to dance in circles in the vineyards, wearing borrowed white dresses, singing "Youth lift up thine eyes and behold her whom thou wouldst choose."
The Bible contains numerous references to dancing. E.g., Ecclesiastes 3:1,4, Lamentations 5:15, Exodus 15:20, 1 Samuel 18:6, etc.
Nahman of Bratzlav believed that to dance in prayer was a sacred command. Many rabbis called for dancing on all festive occasions. Processions and dancing to welcome the Sabbath are a long-standing tradition.
The word in Psalm 150 (and Psalm 149) is mahol in Hebrew. In Modern Hebrew it means dancing. The Jewish Publication Society translates it "dance." The Brown Driver and Briggs Lexicon says it means "dance." Jastrow’s dictionary of the Talmud says it means a chorus of singers and dancers. Klein’s Comprehensive Etymological Dictionary of the Hebrew Language says it is a noun meaning dance derived from the verb HOL, to dance.
Nahman of Bratzlav was an 18th century Hassidic master. The Hassidic
movement sought to bring the emotional element back into a Judaism which
many felt had become overintellectualized.
The kind of dancing he was talking about was meant to be an expression of
"spiritual ecstasy", so I don't imagine it was too subdued. Form what I know
of the Hassidic movement, "subdued" and "dance" do not belong in the
same sentence.
You might check your public libraries for a copy of the "Encyclopedia
Judaica," which contains a fairly lengthy article on dance and what it
entailed.
The Bible's description of the way David danced and "all the house of Israel
before God" contains such words as "jump," "leap,"
"rotate" and "skip," so
it evidently refers to a very energetic form of dance.
Most of the references I have found do appear to be references to dancing
outdoors. Of course, the people at large did not actually enter the
Tabernacle or the Temple proper, but only into its courts.
I would not expect high-energy dancing inside the synagogue, but there are
processions, such as at Simhat Torah. (This ceremony emulates one that once was traditional at the Temple).
Dancing may not always be appropriate, (there is a proper time and a place
for everything), but I can't think of any Jewish authority every referring
to it as "irreverent."