Your first piggy was fine by default not having any other company and therefore becoming human orientated; guinea pigs can't suicide, they just have to make do with their lot in life, whether that is appropriate for them or not.
By not allowing your girl to live according to her species needs your mother is actually breaking one of the basic five animal freedoms that are now official in the UK, the right to express normal behaviour, which includes company of the own kind for group animals.
Sadly in the UK it is only a declaration without yet any legal weight behind it.
http://www.aspcapro.org/sites/pro/files/aspca_asv_five_freedoms_final_0_0.pdf
Tell her that in Switzerland it is forbidden to sell and keep guinea pigs as singles since 2004 (together with all other group species like rabbits for instance), and that fines for shops, rescues and breeders breaking this rule can be quite hefty. Owners are also breaking the law and can be pursued in severe cases.
I am very sorry that you are yet another minor whose parents have not advanced in their mindset from the last century when there has been a great general change in the acceptance of species needs in pets and more of a shift to seeing things from an animal and not just human-centred perspective.
I have just written an article about an in-depth look at single guinea pigs in different situations, possible ways of finding compatible companionship even for the more difficult to match piggies and what extra challenges and responsibilities the keeping of single guinea pigs brings with them when you look at the issue from their species needs. The article is available in the current issue of Guinea Pig Magazine (part 1, issue 48) and in the next coming out in about 10 days (parts 2 and 3, issue 49). The magazine is available in print or as a cheaper download version.
Guinea Pig Mag