If two companies’ patents are to be used together, does one have to be a wholly-owned subsidiary of the other?

No. According to the relevant provisions of the law, patents, as the name implies, are used by whoever invents them. They cannot be used by outsiders at will. Use at will is an infringement and will be punished by law. Patents filed jointly by multiple companies can be used together. It is not necessary that one be a wholly owned subsidiary of the other.