We'll need to treat the two parties in the merger with kid gloves—both clients are extremely sensitive.

I can't stand the way my family always treats my younger brother with kid gloves, trying to protect him from every little thing!

To handle with very gentle care, often to the point of coddling. Kid gloves are very soft leather gloves, typically made from the skin of a young goat (a "kid"). I can't stand the way my family always treats my younger brother with kid gloves, trying to protect him from every little thing! We'll need to treat the two parties in the merger with kid gloves—both clients are extremely sensitive.

treat someone with kid gloves

handle someone with kid gloves

or

If you treat someone with kid gloves or handle them with kid gloves, you treat them very carefully, for example because they are very important or because they are easily upset. Some artists have to be handled with kid gloves and apparently Jake thinks Lotte is one of them. This is someone that you will have to treat with kid gloves. Note: Occasionally, people say that they treat or handle something with kid gloves, to mean that they are very careful about it. Even in presidential campaigns, foreign policy is treated with kid gloves. Note: Kid gloves is used in other structures and expressions where you are describing how carefully someone is being treated. We must take off the kid gloves and smash these evil monsters once and for all. They accused him of using kid gloves to deal with violence and intimidation. Note: People sometimes use this expression when they want to suggest that they do not think this kind of treatment is right or necessary. Note: Kid is very soft leather.

Collins COBUILD Idioms Dictionary, 3rd ed. © HarperCollins Publishers 2012