How do I transfer cable service temporarily?

I babysit at my cousin's frequently, recently I purchased a laptop and we both wondered if I would be able to hook up her cable internet to it while I'm there. I thought it might be possible to unhook it from her computer and put it on mine, then transfer it back in the morning. (I wouldn't want to have both hooked up, I babysit there, I don't live there and I plan on getting the same provider at my own home soonish)

I just didn't want to attempt this without real help.