Gosh OP, you 'prefer' a southern accent? I, on the other hand, visibly shudder when I hear one.
Obviously not, because that would be ridiculous. I live in Glasgow, & there's not really a standard Glasgow accent: do you live in Easterhouse or Dowanhill, Bearsden or Drumchapel? Because they're WORLDS apart!!
I grew up just outside Glasgow & my 3 DC in Glasgow & we all have very nice accents. We do speak quite quickly, as is common, but have perfectly lovely accents. Is it all Scottish accents you have an aversion to? Invernesian has been crowned the 'purest' English in the UK, for example.
Glasgow is a fantastic city with so much to offer- culture, fashion, architecture, entertainment, access to outstanding nature- or so DS1's English flatmates/gf who all chose to be at university here say. I suggest you focus on that, & giving your DC all the best opportunities you can. I'm presently in the stunning Highlands, a mere 2.5 hours' drive away.