I too would hesitate to contact social services.
I would insist that my daughter sat down and listened to my concerns.
These being that she is behaving as if she has no children, the one girl is seriously underweight, and unless she has sole legal custody of both children, she may not, and should not uproot them and move to another country, just because she has fallen in love.
Home schooling is never a really good idea and dragging two children away to what sounds like a nomadic existence is even worse.
If she will not discuss things sensibly, then you may have to contact social services, but unless the father of your granddaughters is abusive, alcoholic, or in prison, I think you should get in touch with him first.
I have never liked the idea of boarding schools, but it sound as if a good boarding school would be the lesser of two evils here.
Would you be able to have the girls living with you for a year or so, while their mother finds out if this new relationship is going to work or not?
If it does not, she will be in Queer Street if she has sold her house and moved in with a man, who may not even want the two girls living with them.
And incidently, what is she planning on living on and supporting her children on? Does she speak Portugese, or can she get a job where English is attractive in Portugal?
If she is British, as I assume, she probably cannot qualify for a job seeker's allowance in Portugal, social security etc. and she may have to pay tax on any assets in the UK both in Britain and in Portugal. Has she thought about any of all this, of found out how she will be placed?