Forgive me if I use a slightly different example, which makes it easier for me to imagine using in realistic conversations. This will show the same issue that you were illustrating.
Vamos a usar el libro mío, que está en la cocina.
Vamos a usar el libro clásico.
How to combine? You're right to wonder how to accommodate two adjectives after the noun. Answer: recast. I can think of a few possible ways:
Vamos a usar el libro clásico, el mío, que está en la cocina.
Vamos a usar el libro mío, el clásico. Está en la cocina.
Vamos a usar mi libro clásico, que está en la cocina.
[Note, Spanish has two verbs that both translate to "is": one that essentially provides a definition, "El libro es azul," and one that describes a dynamic, changeable quality, "El libro está mojado" | The book is wet. That's why I edited your question and changed "es" to "está." You will get to this pretty soon, I think, in your studies.]