Cat goes from friendly to afraid?

So my boyfriend and I have a neutered male that's about 1.5 years old. He's a sweetie but we felt like he needed a pal to hang out with and occasionally play with while we work. (He gets easily bored with balls, strings, boxes, the laser pointer, and even the jitterbug thing I bought him.) We've been scouting the shelter for a couple of months and finally we brought home a petite little female that's around the same age. At the shelter she was super affectionate and fine with other cats. She was apparently removed from the home of a cat hoarder. We brought her home to her safe room with all of the furnishings and she was a little cautious but very friendly and curious. It's been a week now and she's just getting more and more timid every day. I know it takes time for cats to adjust but I've never heard of a loving and seemingly outgoing cat that becomes more skittish and timid as time passes. She spends all day asleep in a box of clothes in the safe room and only occasionally will she even leave the box, let alone the room. I'll be sitting quietly on the computer or the couch and she'll slink out into the living room. I'll softly say her name and she freezes with the "deer in the headlights" look and runs back to the room. All of this seems normal enough but when we pick her up and bring her to the living room and sit her on the couch, she snuggles, and purrs, and is a sweet little lap cat. She will maintain this attitude as long as we don't get up from the seat. The moment we stand up she bolts for the other room. If you walk into her safe room she acts nervous until you start petting her. She then is aggressively friendly and even cries a bit if you walk away. One time she even hissed at me while I was walking away... No arch or ears laid flat, just a hiss. All the while our original cat has been taking it all in and is back to his normal behavior and routine already. (I know this isn't the norm... but it's been less stressful for me to know that he's not miserable .) When we first brought her home our cat got a peek at her and hissed and the like, but she totally ignored him. Now he's moved on to curiosity and wanting to approach her but now SHE hisses at HIM. How could she flip flop like this?! I'm dumbstruck.

I've had cats all of my 25 years and my family used to foster many cats, but never have I seen such polarized behavior like this. She's so hot and cold that it seems like she might be using affection as a submission technique? I'm clueless.

It's been a couple of weeks and with no signs of improvement we've decided to take her back to the shelter. She's a sweet cat and will find a loving home somewhere, but it just isn't destined to be our home. If anyone still wants to reply then maybe someday someone else will find it useful while struggling to understand their odd kitty's behavior.