Yes but your other computer on the LAN is connected to the network so it'll see you already spent your coins.
If disconnect both, in order to get a longer blockchain, you'll have to generate blocks; good luck with that.
BTC difficulty is currently 19,339,258.
You'd need to have 51% of the hashing power, hence why it's called the 51% attack.
You kinda left that step out.
At step 9, you indeed need to generate blocks faster than the real network ... That's why you need some horsepower and that's why it is "recommended" to launch a deny of service on the main pools to ease your chance to get a longer blockchain.
I'm not an expert, but I suppose you don't really need 51% of the hashpower ... the more you have, the more likely you will generate a longer blockchain in a given timeframe. At 25% I suppose you can already be considered a threat
At 25% you would have to be VERY lucky to be a threat. You don't want to have too much more than the network so as not to reflect any huge spike in network hash rate when you broadcast your blockchain.