It's not 'split over'. It's 'spilt over'. 'Spilt' is the past tense and past participle of the verb 'spill'. If something 'spills over' into somewhere, it means that it extends into an area where it shouldn't be. For example, if you spill your coffee, and the coffee pours across the table and on to your books. Your sentences means that your troubles (for example work or personal problems) sometimes affected your family life in a negative way.

This is a picture of water spilling over a dam. It illustrates the meaning of the phrase "to spill over." http://www.abc.net.au/news/image/5804028-3x2-940x627.jpg