As a note, Jasmine, her kid, and Boomer surviving the explosion by hiding in an offshoot tunnel is actually totally believable. Explosions, being airwaves, don't turn corners that well.
While I would start crying more for the death of a baby in a film rather than the death of an animal, I appreciate and simply adore the choice Independence Day made with keeping the dog alive. In a time when dogs in films would usually bite the dust, this film finally said to Hollywood "fuck you, we're not that cruel enough to off a dog."
I don't know why Wil showing up to greet his wife was implausible. He did tell her to meet him at the air force base. So logically it only makes sense that Wil would go there to try and find her.
It actually makes sense that a TV repairman would be able to outsmart the US Government. With the flawed way our politicians have been doing business, it almost seems plausible.