I picked up this tip from a guitar website. Edit: from a professional guitarist on his website. It is his recommendation for learning to play chords well.
To develop speed with chord changing, do one minute changes practice. The idea is to pick two chords in your chord progression of the song you are working on and practicing changing them for one minute. Put the timer on. Strum only once for each chord. On the guitar, i imagine its the same on uke, the goal is to be able to make 60 chord changes a minute. So yes count your changes. Do it every day and pretty quickly you will notice your speed of changing increase.
Before you start the chord change practice, practice getting the sound of the chords right, particularly the difficult chord. So take more time over chord formation and then sound each chord, and strum through once. I hope this is clear. After you've got a good sound coming out of your chord, then you can move on to the one minute changes.
When i learn a song now, i do chord change practice iwth all the chord progressions in the song. More work will be required on the more difficult transitions. This will be the fastest way out there to get good at playing difficult chords.
Oh and the other thing is having an anchor finger or how you make the transition from one chord to the next to make it easier. This is usually dealt with in other beginner courses and some tutorials. If you haven't come across this, others will probably explain it best. Or tell us what chord transition your are currently struggling with and someone will help you think it through.