I agree with everyone else. Even if it is possible to get a second US passport, when you enter the UK using it, you are going to have to answer the IO's questions honestly. Your honest answers might get you bounced, at the very least, and can't be worth being separated from your husband for what, in the scheme of things, is just the blink of an eye...
I also think that if you were honestly just coming to visit on that second passport and were then going back to the US to get your passport with your visa in it...well, if you could convince an IO of that, it might work, but I'd be very surprised. A friend of mine tried that a few years back. She only had one passport, was coming into the country for a couple of weeks to look at houses with her husband, and then heading back to wrap things up in the US and get her visa. Didn't happen that way as the IO had no real reason to believe her when she was actually entering the country with her new husband.