英语翻译The degree to which we identify with an ethnic past will vary according to the strength with which family tradition has maintained that identify ,and to the degree that the family chooses to assimilate into the large society.

maintained that identify 应该是 maintained that identity, 名词that identity 做及物动词maintain的宾语
主干: The degree will vary.
according to 根据，介词
从句： the strength with which family tradition has maintained that identity
同位语从句：to the degree that the family chooses to assimilate into the large society。

我们在何种程度上认同民族过去将根据其家庭的传统一直保持识别强度各不相同，并在某种程度上，家庭选择融入大社会。

我们在多大程度上认同一个民族的过去（一个民族的历史）,取决于两个方面：一是要看家庭传统与这种身份之间所保持的紧密程度如何,二是要看该家庭自己选择在多大程度上融入（同化）到这个大社会中.
另外请楼主确认一下：第二行中maintained that identify 是否有误,末词是identify（动词）还是identity（名词）,仅一个字母之差.

我们对以前的民族的认同程度根据其对家庭传统保持认同的强度各不相同，也取决于家庭选择融入社会的程度。