Yes there's no night trains in Spain. The route between Milan and Chambéry is closed due to a landslide, you have 2 alternatives :

- via Geneva

- via Nice

The route will have to be done in 2 days. It's better to sleep outside of Spain so you don't have to use the 2 inbound/outbound journeys at once. For example (there are a few other options) :

From Sevilla to Milan :

Day 1 :

- AVE Sevilla Santa Justa - Madrid-Atocha 09:36 - 12:12 10€

- AVE Madrid-Atocha - Nîmes 13:25 - 20:22 10€

Day 2 :

- TGV Nîmes - Lyon Part-Dieu 06:59 - 08:24 10-20€

- TER Lyon Part-Dieu - Geneva 08:38 - 10:46 or 09:38 - 11:46

- EC Geneva - Milano Centrale 13:39 - 17:40 13€ (also possible to leave at 12:10, arriving at 16:40 via Brig)

From Milan to Sevilla :

Day 1 :

- IC Milano Centrale - Ventimiglia 07:10 - 10:54 or 2h later 3€

- TER Ventimiglia - Nice-Ville 11:17 - 12:10

- TER Nice-Ville - Marseille St-Charles 13:25 - 16:06 or later

Feel free to stop in Nice for a few hours.

Day 2 :

- AVE Marseille St-Charles - Madrid-Atocha 08:04 - 15:45 10€

- AVE Madrid-Atocha - Sevilla Santa Justa 16:00 - 18:42 or 16:30 - 19:03 10€

With this itinerary you avoid the expensive cross-border TGV (25-35€).

Prices above are for reservations with an Interrail pass. Reservations for the cross-border AVE are only available at RENFE ticket counters (10€). For other trains have a look at : https://www.seat61.com/interrail-and-eurail-reservations.htm (most can be done on interrail.eu but there are extra fees)

I don't have experience travelling with a cat but it shouldn't be an issue anywhere. On the other hand dogs are more problematic.

What would be your travel dates ? Trains around Christmas & New Year will be very busy and should be booked ASAP.

Questions welcome of course.