うち here doesn't mean "house", but "our", e.g. "our kids". (see also: うちの人 ). Often used as "our" when referring to one's own family, but can be used for other cases (e.g. うちの社長).
For べったり, think attached as in being clingy, in this case enough that it's a bit of a problem (困る).
(I don't believe in exact translations, but you get the gist, I hope).