I agree with your instinct, and I think in your shoes I'd make it an "either / or". In other words, say to the letting agent "I am happy to rent the house to your family member, but on the condition that I switch the management of the property to another agent to avoid the conflict of interest that would otherwise arise."

On the plus side, the agent has at least declared this situation to you - presumably she could have just not mentioned that she happens to be related to the proposed new tenants. You should thank her for that and perhaps explain that you will switch the property back to her management once her family members have moved out in the future.

I agree with your instinct, and I think in your shoes I'd make it an "either / or". In other words, say to the letting agent "I am happy to rent the house to your family member, but on the condition that I switch the management of the property to another agent (at another management company) to avoid the conflict of interest that would otherwise arise."

On the plus side, the agent has at least declared this situation to you - presumably she could have just not mentioned that she happens to be related to the proposed new tenants. You should thank her for that and perhaps explain that you will switch the property back to her management once her family members have moved out in the future.