The two trees mention in Gen 12:6 and 35:4 are unlikely to be the same tree as their Hebrew word is different. However, it is more likely that it the same tree mentioned in Judges 9:6, 36 where Joshua condemned idol worship.
Note the comments of Ellicott in Gen 35:4 -
The oak.—Not Abraham’s oak-grove (Genesis 12:6), referred to probably
in Judges 9:6; Judges 9:37—the Hebrew word in these three places being
êlôn—but that under which Joshua set up his pillar of witness (Joshua
24:26), the tree being in both these places called allâh, or êlâh, a
The Cambridge Commentary is similar:
the oak] R.V. marg. terebinth. It is noteworthy that Joshua, under the
same “oak” of Shechem (Joshua 24:26), testified against the primitive
worship of strange gods; cf. Joshua 24:2; Joshua 24:14; Joshua 24:23.
For the “terebinth,” cf. Genesis 12:6. The same sacred tree is
possibly mentioned in Jdg 9:6.