We have to trip a contactor and a fused disconnecter from a relay. Should we first trip the contactor by 125 V DC output from relay and then contactor trips the fused disconnector by 125 V DC? Or should we trip both contactor and fused disconnect directly from 125 V DC output from the relay.
I'm not sure of what you are describing here. A contactor is not a "trip" device, it is a "control" device. So you can ENERGIZE a contactor, or you can DE-ENERGIZE a contactor, but you cannot "trip" one.
In addition, most "disconnect switches" are manually operated devices. Only a select few versions have a "trip" mechanism, the most common LV one being what is called a "Pringle Switch", or a "Bolted Pressure" switch (although not all will have trip coils either). Or you are talking about MV Load Break Switches in MEIS (metal Enclosed Interrupter Switchgear) equipment, or you have a main Line Contactor Unit on an MV MCC that has a Line Contactor and a fused "Isolation Switch", in which case the switch would NOT be rated to disconnect the load directly, it works in CONJUNCTION with the contactor.
So because those all have different scenarios regarding how you would accomplish the opening of the power circuit, you will have to do a better job of helping us understand what you have if you want help.