One lesson here is that different countries have very different legal systems. A "suspect" in portugal is very different from a suspect in USA, UK etc... it means that the person can be open to a different line of questioning and have a lawyer present etc..
There was another man potentially involved a few months back and he volunteered himself as a "suspect", I believe. Not 100% sure about that, but I am sure that suspect does not mean exactly the same thing as we take it to mean.
However the mother is considered to be a suspect in the way we know it.
In portugal the police cannot give away any information, therefore speculation is high regarding everything.
The parents were stupid leaving their kids alone especially at that age, in a resort with access to childminding facilities. Nevertheless, you could leave your kids with a babysitter and they still get killed/kidnapped. HOWEVER these were little kids, I'd be worried they go into the kitchen and stick forks in the electrical sockets or who knows what.
The parents and people they were dining with were taking turns going to check on the kids. One of the other parents noticed a man carrying a child in a blanket on one of her trips. Egads!
The other lesson here is portugal has inept policing. The scene was open to all and sundry. Evidence was collected late. Forensics seems to be an unknown discipline. I would not be surprised if the police were in on a child trafficking racket. They seem to be badgering the mother for 11 hours to get a confession so they can close the case. When you go to a foreign country don't expect the same levels of competence as your own country.
This is very much turning into the UKs' own Azaria Chamberlain incident ... in Oz, a couple claimed that, when camping in the Australian outback, a dingo took their baby from the tent (silently!) and the whole investigation was a mess spread over decades.
don't take your baby to the desert and put it in its own tent.
don't leave your 3 year old kids in a strange hotel in a foreign country as you go get drunk
don't expect foreign countries to be the same as at home