I find accents fascinating, so I'm glad to have found this thread!
I'm Glaswegian and DH is from the SE.
DS1 was 6 when we moved from Glasgow to Yorkshire to set up home together. He developed a strong Yorkshire accent very quickly, as his classmates were bewildered by his Glasgow accent.
DS2 arrived five years later.
When DS1 was 12, and DS2 was 1, we moved to London. DD arrived a year later.
We spent 7 years in London. Both DS's had a London accent, as did DD when she began to talk.
When DS1 was 18, he went to Newcastle University where he's stayed ever since (he's now 25). He now has a strong Geordie accent.
When DS2 was 7 and DD was 6, we moved back up to Yorkshire.
DS1 is now 16 - he still has a Southern accent (was born in Yorkshire)
DD is 15 - she has a strong Yorkshire accent (was born in London).
I still have a strong Scottish accent.
I'm not sure why DS1 and DD have been influenced by the local accents, but DS2 hasn't?
We went on a family holiday in the summer, and DD got friendly with a girl from the Midlands. Within days, she was talking with a Black Country accent.