If your wife is to avail loan from her bank then she has to be a co-purchaser in the sale agreement, otherwise how will the bank sanction the loan?
It is permissible u/s 54 of income tax act that the family members of the assessee by whom capital gains tax is payable, can be included in the sale agreement for sake of convenience
Just because family members are included as co-purchasers is no ground to deny the capital gains tax exemption
But then there will be logistical issue because how will the newly purchased flat be collated to its actual owner
So what can be done is, you and your wife can become co-purchasers in sale agreement where it will be clearly written that you both are being included only as a part of family arrangement and for convenience sake and no ownership right is being conferred on the co-purchasers
Then your wife can pass on the loan amount to the seller on behalf of your father and it will be stated in sale agreement that the EMIs for the loan will be repaid by her or you and such emi shall be considered as gift to your father (which is also permissible u/s 56 of income tax act)
In this way you can continue with bank accommodation and avail capital gains tax exemption