Building strength and skill to tackle chords..what worked for you?

I have been gradually improving playing mostly Irish tunes from the Berthoud Irish Mandolin book. Ive got a guitar and fiddle background, this is the most enjoyment I have ever had playing an instrument, but wow..these chords. I don't remember guitar chords being this challenging. For instance I picked up the chord progression for an old folk song I used to sing for my daughter when she was a baby, "I've got a mule and her name is sal.." Its low enough that my lousy pipes can handle it..but whoa..Em A B7 G? The only thing in there I can touch is the Open G. I have very small hands for a guy, just the effort needed to go for the G and D string for the A chord with one finger is almost out of my range, and lets just say what I can get has lousy tone..

So I guess what I am asking is..Is this a typical issue? Did you gradually work up your chords? Is there a (start here these are easier for beginners) set of chords? Should I consider one of those gripmasters? I am thinking the action is high on this mandolin, but I 'd rather slug it out for a while and build the strength then lower it or switch to light strings.

So what did, do you do to work those skills up? What worked for you? Thanks!