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With help from Posva from Vue I was able to solve this.
My approach and understanding of how Vue Router worked was slightly incorrect by thinking that you needed to reference the named route in a nested tree that you wanted to update.
To update the Transport type in /euope/spain I would need to instead reference the Country named route and update the param for the transport.
<router-link :to="{
name: 'Country',
params: {
transportSlug: filter.slug,
}
}">
This maintains the correct URL while updating the Transport type.
Hope this may be of some help to someone.
Source:stackexchange.com