Valery, I had good luck driving the moles away by just sticking the hose down their holes and flooding the tunnels. But Jean's absolutely right, they are there because you have some insects in the lawn that they are feeding on. If you don't want to spend money and nuke your ecosystem using a broadcast lawn insecticide, flooding the tunnels is the best non-toxic way to drive them away. Next you need to change your mind about lawn.
The environmental thing to do about lawn here is to simply "mow what grows". The grasses that grow here are not very nice for lawns, unless you are looking at them from far away. You'd no sooner walk on St. Augustine grass in your bare feet than . . walk on gravel, jmho.
The huge amount of labor, chemicals, machinery and water it takes to grow a 'beautiful lawn' are just the reason to reduce the amount of lawn you have to the bare minimum. Everything you do to grow beautiful fine-bladed grass here is bad for the environment, not to mention really expensive and labor intensive.
The concept of a gracious garden having expanses of lush green lawn came from England where, as you say, nice grass grows easily. That simply doesn't apply here in Florida. It's chemical warfare to try and grow a lush lawn, and will be an exhausting, ongoing battle. You'd be much better advised in the long run to spend all that chemical money on shrubs, trees, perennial native flowers and mulch. Reduce your lawn area a square yard or two at a time until you just have pathways of grass to walk on, for the dog to run on, etc. and your life will be much simpler and less work. Not to mention it will be 10 minutes of mowing twice a week in summer, not an hour or two.
Sorry, putting away my soap box now . .
