Will UAE courts recognise a will I made in my home country?

Possibly, but it isn't straightforward. A home-country will may be recognised for UAE assets only after legalisation, certified Arabic translation, embassy attestation and a formal UAE court application - a slow, discretionary process that isn't guaranteed and can still end in Sharia distribution. Registering a DIFC or ADJD will for your UAE assets is far more reliable. Seek legal advice.