Feel free to use the water squirt bottle, just as with the cats. It works well with dogs also, and they don't see it as "you" reprimanding them. It's "rain from the ceiling," I guess.

I think you did right putting him in a time out. Sort of like NILIF.

He may have been jealous that she was getting too close to HIS mommy; or maybe he was showing he is dominant over her.

Not sure what more to suggest. Hang in there!