I think you are misunderstanding what the developer is trying to tell you.
They are not saying you need to provide the full data set to the user, but that you need to apply the sorting before the pagination is applied. This is absolutely correct, and you should not support client-side sorting if you have paginated data - it will be incorrect and misleading.
If you are willing to sacrifice some efficiency and accessibility you could try a node based UI. Connecting nodes with drag and drop can be fun and visually rewarding, but only if the number of nodes are small.
When you find yourself stuck on one design, strip the task down to its essentials as defined by your user research. In this case, it seems you need to support:
Users specify a Target C node.
User specify a Source A or B node to go with it.
Display the resulting Source-Target relation.
Surely there are many designs to accomplish each step and combine them....
There might be a specific use case where it makes more sense to select the date and then applying it to multiple rows but typically you would be selecting multiple rows and applying a date to it.
This is because the process of selecting a date through a calendar widget (or entering it directly) involves a little bit more thinking and processing, which means ...