You appear to be asking about the usability of relative adverb 'that' in place of relative adverbs 'where' and 'when'. The answer is that, while this is sometimes possible, or even desirable (e.g. the day that she arrived instead of the day when she arrived), most speakers would probably not find it entirely acceptable with regard to either of these examples.
Note also, from an analytical viewpoint, that whichever adverb we may use, the clause constructed remains an adjectival relative (a.k.a. attributive) clause. An appositive clause is quite different.