sound like queen palms, considered to be an environmental weed as their seeds germinate readily when spread around the bush by fruit bats.

most likley not going to be hugely successfull growing plants underneath them as you have noted they have a very strong root system.

as the palms aren't realy doing that much maybe you should consider their removal and then plant your other food trees which in turn will give "vertical accent" to your garden.

len

Here is a link that might be useful: len's garden page

Thanks for the answer! Now it's much easier as I know the plant species.I'm actually digging up these small palms you see everywhere. Reading the news at the moment makes me feel that we need as much food plants as possible in our garden.
I will have a look if it's really queens palms.
However it's always difficult chopping trees down.

if they have orange/yellow fruits and are germinating readily where they fall they will be queen palms, that's what makes them and environmental weed.

and it won't be like simply cutting trees down you are planning on planting other trees of more enviro' friendly nature, and of food value. after all the palms are an exotic species.

len