I do not see any obstacles in using one child's first name as their sibling's middle name.
After all the time we all spend picking names for our children, other than when they are first born, we never use their middle names while they are growing up unless we are filling out forms that ask for their middle name.
Therefore, using the same first name as a middle name for siblings is really not such a big deal.
As a matter of fact, when the mortality rate was high, it was not uncommon for parents to name a new born baby after a deceased child. My grandmother, who was born in 1913, had two sisters die before they were one year old. Both of them had the first name of "Mary" (different middle names). Then she did have a sister who lived, also named Mary. (personally, I think that was going a bit far in sharing names, but it was popular over a hundred years ago.)