void doc_retree(const document::ptr &doc)
    {
        // PERF check if it hurts
        doc->m_root_render = doc->m_root->create_render_item(nullptr);

        if (doc->m_root_render)
            doc->m_root_render = doc->m_root_render->init();
    }

    void change_parent(const element::ptr &el, const element::ptr &new_parent)
    {
        document::ptr doc = el->get_document();
        element::ptr old_parent = el->parent();

        if (old_parent)
            old_parent->removeChild(el);
        if (new_parent)
            new_parent->appendChild(el);

        if (old_parent)
            old_parent->compute_styles();
        if (new_parent)
            new_parent->compute_styles();

        doc_retree(doc); // PERF optimize this by request a call that be applied when renderering
    }

instead of using element->appendChild(), you need to use this custom change_parent which will ensure the document render tree is updated after changing a parent of element, I guess.