safe for mom and 18 year old daughter

Have you considered taking a short flight from Madrid to Lisbon (say via EasyJet, etc.)? They should be quite inexpensive on a budget carrier and will save you a lot of travel time. In general, trains are safer and more convenient than passenger vehicles. Renting a car would incur large drop off fees because you're planning on traveling from one country to another...then you'd have the parking issues in Lisbon and the car would end up just sitting there since you won't need it. That would be my least favorite option after travel by air, bus, or train.

Once you're in Portugal, you shouldn't have any hesitation with using trains.

You need have no concern whatsoever (says the person who spent two weeks traveling with her 70-year-old mother in Morocco in the late 1980s). Seriously, you'd be fine anywhere in Europe, and Portugal seemed particularly laid-back on my two visits there (many years ago, I admit).

Transportation between Spain and Portugal can be a bit more complicated than one might expect from looking at a map. Have you figured that part out yet?

Agree with Agnes. A quick check of flights from Madrid to Lisbon next June is showing one-way fares of $38. Takes 1+15 hrs...probably your best bet.

Personally I always feel safer taking a train or bus than driving.

I too would feel safer on the train than driving, where luggage security in a left car is a constant stress.

Fly from Madrid to Porto, then take the high speed train to Lisbon, with an overnight stop in Coimbra on the way. Take time to check out Sintra from Lisbon.

I know planes are so darn cheap now but using planes for these jaunts is so much worse for the environment- take the train please.

It looks like you could take a two bunk compartment with private shower and toilet on a sleeper train. There are no daytime trains from Madrid to Lisbon. I would feel more comfortable on the train than driving even in a four bearth compartment. http://www.seat61.com/international-trains/trains-from-Madrid.htm#Spain-Portugal I like night trains but haven't been on one in Spain.

As far as safety on trains or in Portugal generally - have no concerns. I've lived here solo for 15 months, traveled on trains solo, driven, etc. I've never felt in danger. I feel much safer in Portugal than I do in the U.S.
Regarding the night train from Madrid to Lisbon - I've heard vastly different reports from people who have done it. Some people say it was terrible because it stops so frequently - preventing good rest over night. But, then others say it was great! Read lots of reviews before making your decision.
A flight is likely the easiest and quickest.

I am curious about what safety issues you have with regard to train travel in Portugal.

We're traveling through Portugal and Spain JFK-LIS rt. We found an inexpensive flight from Seville to LIS at the end of our Spain trip.