Allocating time between Madrid and Lisbon

I'm just wondering about the 2 nights in the Algarve. You don't say what time of year you are traveling but if it's beach weather, there are beaches much closer to Lisbon. You could split your time evenly between Madrid and Lisbon and really do each city justice. As there are day trips from each city, you could easily fill your days without the added expense and hassle of driving to the Algarve for only two days.

Some people find it impossible to sleep on overnight trains. I have no idea how smooth the rails are between Madrid and Lisbon, but if they're like what I experienced in Italy last year, your train trip may be miserable and the drive to the Algarve unsafe.

Why take the uncomfortable overnight train to Lisbon to then drive straight south? As has already been said, this is dangerous if you haven't had much sleep.

Fly direct from Lisbon to Faro, then hire a car. If you are only visiting the Algarve for the beaches, then scrap the Algarve and visit some of the great beaches on the Atlantic coast closer to Lisbon, which will save a lot of time. When are you visiting?

You could hire a car in Lisbon and take a short road trip round some of the inland towns instead of going to the Algarve - such as Evora, Tomar, Obidos etc. Sinatra and Cascais are easily covered by train from Lisbon.

I'm not sure when your trip is, but you might consider flying from Madrid to Faro, pick up a car, then after spending time on the Algarve, drive to Lisbon and drop the car. As others have reported, overnight trains are not the most comfortable option. Air Nostrum has direct flights for under $100 if booked ahead. For example in early October, they fly from Madrid to Faro on Fridays-Mondays only. See www.skyscanner.com for options. Even if you took a flight that changes in Lisbon, the trip would be faster and cheaper than train & car.

It is easy to fly from Madrid to Lisbon. Rick has a website with descriptions of discount intra-european airlines. It is probably less expensive to fly than take the train, and much more comfortable.
Given your time constraints you might consider beaches close to Lisbon to save on travel time.
Sintra is an easy day trip from Lisbon.

Drop the Algarve. You can go to the beach anywhere. Skip it.
Lisbon and Madrid are great. From Madrid, you can visit Toledo and Segovia. With those cities, I recommend five or six days there.
Lisbon, go for three nights and more if you visit Evora, Sintra, Obidos and https://en.wikipedia.org/wiki/Batalha,_Portugal