If I understand you correctly, the reason for the gate is to SLOW the traffic down? If a gate dosn't work by reason of non co-operation by the neighbour, I would consider traffic CALMING, i.e. put in an unavoidable speed hump
. But, to safeguard against any possible claims for damage or injury, it would be prudent to put up a sign - 'Warning, speed hump' that is clearly visible from both directions. I would also pen a polite note to the neighbours (keep a copy) informing them of the presence of the speed hump - so they can't say they havn't been told.
This may however cause a deterioration of neighbourly relations - be warned!