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Legally, there is no reason you should not do this, but you do need to understand why they're asking you to do it.
If there is no good reason, then you might be a little concerned as to whether it's all genuine.
I agree that the request sounds a little odd, but if you're going to be contracting with the main parent company, then you might feel more comfortable with it. There is nothing stopping the parent company (with whom the contract might be with) from sub-contracting its works out to somebody else, but it remaining responsible at all times for issues concerning the kitchen.
This was, you remain as protected as you can be, against the subsidiary going insolvent and not being able to deliver your kitchen etc.
The obligation (if the contract is with it) would be with the parent to do the works.
If they want you to contract with the subsidiary and not the parent, but to pay the parent, then I would feel uncomfortable about that.