You could probably simplify the relay portion of this by using one of these high current motor drivers (with the note you may need to add a bigger electrolytic capacitor to the input stage if your motor wants more than 1 a or so) for around $5
The limit switches being in software is a bit dangerous. I prefer the limit switches to be in series with the motor so if the processor fails and the motor hits the limit switch the power shuts off to the motor independent of the processor. If you keep the relays, in series with the relay coil that provides power is also an option (although there is still the risk of the relay contact sticking in this case). There is the complication that the limit switches need to be arranged so that if one is tripped the motor can still move the other way though. As well on the software side you may want to consider security if you haven't already. Is it OK if just anyone that connects can open the gate? It may be, in which case no security is fine but if not then you need to figure some method of authentication (which often gets forgotten til too late 
). Assuming this is outside somewhere, you may also need to consider temperature. Most electronic devices stop functioning (unless they are special wide temp range devices) somewhere a fair bit below 0 and you may need to consider that if you have cold winters wherever this will be and it needs to work in winter.
Peter