This notably differs from the example in OP by its position outside of the first sentence. AFAICT, your second sentence cannot function as a parenthetical like the example with "which motion".
> The local cafe that my dad loves has a lot of lunch options.
> The local cafe, which my dad loves, has a lot of lunch options.
But British English generally uses "which" for both:
> The local cafe which my dad loves has a lot of lunch options.
The "cannot function as a parenthetical" is essentially what a restrictive clause is, although of course the person you're replying to broke things into two sentences.
*Upon the submission of the cause the appellant made a motion (to amend its assignments of error) that motion is now granted.
The current ungrammaticality of the original example given in OP is due to the presence of "motion" within the wh-phrase (c.f., "Which motion is now granted?"), which does not have an equivalent construct for restrictive clauses using "that".