Is it permissible for two people to do ‘umrah on behalf of one deceased person at the same time?

Yes, it is permissible for two people to do ‘umrah on behalf of one person, even if that is at the same time, because each of them is doing ‘umrah independently of the other, on behalf of that person. 

Ibn Qudaamah (may Allah have mercy on him) said:

If he appoints two men to do Hajj on his behalf in the case of the obligatory Hajj, Hajj in fulfilment of a vow, or a voluntary Hajj, then whichever of the two enters ihram first, his Hajj will count for the obligatory Hajj, and the other will count as a voluntary Hajj, or in fulfilment of a vow, because he cannot do any Hajj before the obligatory Hajj, and the same applies to one who is acting on his behalf.  (from al-Mughni (3/104))

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

Question: is it permissible for a man to appoint more than one person to do Hajj on his behalf in the same year?

He replied: That is permissible, but if he appoints two or more people to do an obligatory Hajj on his behalf, then which of them is doing the obligatory Hajj on his behalf? The answer is: the one who enters ihram first, and the second Hajj counts as naafil (supererogatory). from ash-Sharh al-Mumti‘ (7/33) 

Based on that, it is permissible for you both to do ‘umrah on behalf of your deceased loved one at the same time, so long as each of you does his or her ‘umrah independently of the other, intending to do ‘umrah on behalf of the deceased. 

And Allah knows best.