its owner seated in it是过去分词独立主格结构,做伴随状语,修饰主句动词was；而playing bridge with children是现在分词作伴随状语,修饰seated.
这里牵扯到seat的用法：seat是及物动词,意为“使坐下”,普通要说He seated himself或Please be seated.
这个句子主干很简单,就是个there be结构there was a gardon,谈不上主谓宾的划分.确切地说,there was a garden是个倒装结构,garden是主语,was是谓语,there是表语.
主句的主语是garden,过去分词结构的主语与主句主语不一致,是owner,这就是过去分词的独立主格.学语言要靠多听多读来提高语感,不要被概念术语搞糊涂.分词作状语时,如果其逻辑主语与主句的逻辑主语不一致,就用到分词的独立主格.比如I seeing from the mountain top, the cars are small中,现在分词状语的主语是I,主句主语是cars,这就是现在分词的独立主格.如果说Seen from the mountain top, the cars are small,过去分词状语的逻辑主语和主句的逻辑主语一致,都是cars,就不用独立主格.
提醒：要想用whose,得说成whose owner was seated in it；要想用which,得说成in which its owner was seated.
——【译苦思甜】团队成员荣誉回答