Double Flats

Ruined my day of riding by getting not one, but two flats. The first one was from hitting a sizable rock straight on, the other from an industrial sized staple. To make matters worse my Topeak Race Rocket pump kept unscrewing the inner tube valve core, deflating my tire at least 10 times. I remedied the problem by using the glue from my patch kit to keep it in place, followed by some saliva on the valve adapter of the pump as a lubricant. Fail. Can anyone recommend a small size pump like that? I'm thinking of a Lezyne.