I'd try a pelham...and some ponies go better in a mullen mouth pelham, and some prefer a jointed pelham. I find that kimberwickes often horses/ponies don't like. Anyhow, if the pony still has problems with getting the tongue over it, there are ported pelhams, or use a rubber bit port. But if the kimberwicke you are using has a solid mouthpiece, try a jointed pelham. I find that kids do just fine learning to handle two reins...I've got some schoolies that are happier in a pelham than a snaffle, and have never had a problem with the littlest kid learning to use two reins.
Had a similar problem with a small last year. Kimberwicke was OK but didn't want to show in that and not that keen on those bits really. Went with a Dr. Bristol with a slow twist, in a full cheek. Was a challenge to find one small enough! Works a charm and the pony has gone from extremely strong/tough to jumping around on a loopy rein at times and lovely and soft on the flat.