Analysing the lyrics

Happiness hit her like a train on a track
Coming towards her stuck still no turning back
She hid around corners and she hid under beds
She killed it with kisses and from it she fled
With every bubble she sank with her drink
And washed it away down the kitchen sink
As the lyrics state, happiness literally hit her unexpectedly, just like when you see a train go back, it appears to hit something really quickly.
She is clearly scared of something, as she wants to hide anywhere possible.

The dog days are over
The dog days are done
The horses are coming
So you better run
The dog days are like a metaphor for the unhappy and disappointing days in her life, she is saying that those days have gone, and now instead the horses are coming, a metaphor for freedom, so she is running with them.
Run fast for your mother, run fast for your father
Run for your children, for your sisters and brothers
Leave all your love and your longing behind
You can't carry it with you if you want to survive
Her family are almost a burden for her, and if she wants to move on with her life, she cant carry them with her, so she has to run away from it. Not necessarily because they are bad, but just because she needs to move on and let go.
The dog days are over
The dog days are done
Can you hear the horses?
'Cause here they come
Repeating about the bad days, and how they are gone,  also more repitition about the horses, and how they are almost there.
And I never wanted anything from you
Except everything you had and what was left after that too, oh
Happiness hit her like a bullet in the back
Struck from a great height by someone who should know better than that

The dog days are over
The dog days are done
Can you hear the horses?
'Cause here they come

Run fast for your mother, run fast for your father
Run for your children, for your sisters and brothers
Leave all your love and your longing behind
You can't carry it with you if you want to survive

The dog days are over
The dog days are done
Can you hear the horses?
'Cause here they come

The dog days are over
The dog days are done
The horses are coming
So you better run