I finally cracked it!
I took my woodsplitting wedges, but they didn't do anything for me at all. So then I tried hitting the back of the axe head with the back of the block splitter and it worked a treat! I can now split wood with hardly any effort at all!!! Except for the really hard wood. There was one hardwood block I hit about 200 times and it just wouldn't split. So we just left those and used them when the fire was hot enough.
When one day I mentioned to my nearly 6yo daughter that a male friend was joining us for a couple of days at the end of our stay, she replied: "But we don't need him to come anymore because we can now chop wood ourselves." :D