I had the opportunity to put 50 rounds of FMJ through a rental S&W 380 Bodyguard. The trigger is stiff but smooth enough to be usable. The gun is DAO which is a good thing since light strikes requiring a second pull were common. The slide is supposed to lock back after the last round. Usually it did but laying the gun down was often enough to release the slide. With my relatively small hands (I shoot my M&P 9 with the smallest grip insert.), the Bodyguard grip is 2-1/2 fingers long. I don't know if there is an extended magazine with room for all three fingers.
I looked at, but didn't shoot, an LCP. It is definitely a two-finger gun. I have heard of an extended magazine which might have room for three fingers.
I have handled, but not shot, a Kahr CW380. With the 7-round extended magazine, its grip is long enough for three fingers but the gun still disappears in my front pants pocket. The CT380, which has a full length grip surrounding its 7-round magazine, might also be small enough.
Another gun to consider is Remington's DAO RM380. A bit bigger than the others, it may be marginal for pocket carry.