Well, we've had Molly for a few days now, and in a lot of ways she's a great dog. She's completely housebroken, has never had a single accident, and she's intelligent (she learns everything really quickly) and very sweet. There is one major problem that we can't find a solution for. It's the previous furry inhabitants of the home - our two cats. Molly chases them without fail whenever she sees them. We had them shut up in one room for the first 4 days Molly was there, and we felt so guilty because they didn't get to interact with us at all and they're used to spending a LOT of time with us. So we thought we'd try an upstairs/downstairs solution with a baby gate, giving the cats free roaming upstairs (especially at night when we're sleeping, because they've always slept with us) and the dog free roaming downstairs.
Unfortunately, Molly stands at the top of the stairs and freaks out when the cats are out, and when they hide, she stands there and whimpers. She did it for 2 hours last night. We then took her downstairs and gently put her in her crate and soothed her, then went back to bed. She went BALLISTIC down there. Which is weird, because she likes her crate and hasn't shown signs of separation anxiety before. Eventually, we had to shut the cats up again and let her upstairs with us, which I know reinforces her bad behavior, but it was 2AM and we had to get up at 7.
My husband is really of the opinion that we should just open up the baby gate and let them meet each other. Molly is 1 year old (the vet confirmed, along with telling us she has hookworm and mange - she's being treated for both) and still has a lot of puppy in her. Her reaction to the cats isn't agressive, more like wanting to chase and play.
I am worried about safety of both dog and cats. I know dogs that have been partially blinded by a cat's swipe, and both of ours have their claws. I'm also worried about the other way around - if the cats start to run, Molly's kill instinct could kick in, even if she's been trying to be playful prior to that moment.
I don't know what to do, but we are exhausted and feeling guilty about all possible scenarios. HELP!
And new pics:

