Application of sale proceeds under specific legacy

A testator leaves four children. Her Will leaves a Property to child 1 and his daughter X under a specific legacy. Other assets are left to the other children by specific legacies. The residue passes to all four children equally.

There are insufficient assets in residue to meet all IHT due. Any excess is, under the Will, to be borne by the four children equally from their specific legacies. The specific legacy to child 1 and X is the only legacy capable of generating funds now (ie the executors are in a position to sell the property - other properties are abroad and subject to other issues which will take longer to resolve).

The sale proceeds will not satisfy the total balance of IHT remaining, but will go a good way to doing so. However, will the executors be able to use all the sale proceeds in part settlement of the IHT, or are they limited to only using the proportion to be borne by child 1? Child 1 is likely to become very unhappy if he receives nothing from the sale proceeds, even if he will receive his entitlement from the other assets in due course.

I hope I have expressed that clearly. Any guidance would be greatly appreciated.