How to make the HT12E transmit (TE to low) only when one or both buttons are pressed?
It may be easier than you think; if you look at the data sheet more closely: -



So, any button being activated will automatically pull TE low and enable transmission and, in the case when buttons are released (thus deactivating TE), this diagram tells you that the device will continue to transmit the four byte message and thus inform the receiver that buttons are deactivated: -