Norse mythology did not concentrate on symbols, but rather on personification. The powers of nature and the elements were portrayed as finite gods. There is no symbol (sign) in Norse mythology for family, however, if the word "symbol" is taken to mean symbollic (meaning "representing of") then the Goddess Freya would be a likely candidate. Among other things, Freya (Frigga / Frig / Frey, etc) was the wife of Odin and was known as the living embodiment of the mother figure. By stretching the meanings of "Family" and "Mother" to meet in the middle, it is possible to see how Freya might be viewed as personification (hence symbolism) of the family. In this case, it is down to artistic interpretation.
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Yes, there is. The Celtic symbol for family is a tree, entwined with flowers. The Celtic knot is very well known and many people use it.