We know that in general, there is no smooth manifold structure on $Hom(X,\, Y)$ where $X$ and $Y$ are smooth manifolds, but under *certain nice conditions* (see https://ncatlab.org/nlab/show/manifold+structure+of+mapping+spaces) we can give a smooth structure on $Hom(X, \, Y)$.

Let $\mathcal{G}$ and $\mathcal{H}$ be two Lie groupoids. Now let us consider the category $Hom(\mathcal{G}, \, \mathcal{H})$ whose objects are homomorphisms of Lie groupoids and the morphisms are smooth natural isomorphisms.

Question 1.Under what conditions on $\mathcal{G}$ and $\mathcal{H}$, we have a (canonical) Lie groupoid structure on $Hom(\mathcal{G}, \, \mathcal{H})$?

Question 2.Is $Hom(\mathcal{G}, \, \mathcal{H})$ always a diffelogical groupoid in general?

It would be also great if someone can suggest some literature in this direction.