From what I read in your message, the problem isn't the estimation itself but the whole organization of the team with DC and Devs in charge of PO's responsibilities. So, that middleman shouldn't exist and PO should finish the requirement documents after DC gives requirements to PO. You still work with DC, just in a more organized way.
This answer I'm providing was crafted with the book How to Kill the Scrum Monster: Quick Start to Agile Scrum Methodology and the Scrum Master Role as base, which I think will deal with your problem from the root.
From Waterfall to Agile (Why you work the way you work)
"The issue with this (Waterfall) methodology is that if a project has a big scope, it might take many months if not years until we get final results. A lot of things can change and go the wrong way. Sometimes during the final stage of acceptance and testing, we might discover that the original design stage was wrong. The success rate of a big project executed in this way is alarmingly low"
Overview of Agile Methodologies
"There are three most common methodologies/methods to implement Agile principles: eXtreme programming, Scrum, and Kanban."
Agile Scrum Deep Dive
"The Product Owner (PO) collects requirements from customers (internal or external) and produces the requirements documents. The PO constantly aligns with customers and determines the scope of work and change in the scope, so the PO will get results from the Sprints. The PO is responsible for providing all the necessary product-related information required by the team and providing requirements.
The Scrum Master ( ScMa ) is the servant-leader of the team who helps the team to deliver based on requirements. The ScMa organizes the process and moderates the meetings that will enable the team to deliver. Also, the ScMa provides statuses to the PO or any stakeholders. The ScMa is in charge of resolution of any block and impediments the team faces. The ScMa shelters and protects the team from external teams and stakeholders.
The performance of the individual team members and other HR topics are not the ScMa’s direct responsibility. There is another role Line Manager that is responsible for the performance of individual team members. Line Manager is direct manager for all the members of the Scrum team.
The Architect (Arc) is the technical lead in the team. Often, most of his or her time will be dedicated to guiding other team members, rather than individual tasks. The Architect creates/approves design, reviews code, and works in close sync with the ScMa and PO.
Not every Scrum team has an Architect; however, at least one senior developer on the team should have profound expertise on technical aspects of the work.
The Quality Manager (QM) or Quality Engineer(QE) is the team member responsible for quality management of the product. The QM organizes the quality process in the team, educates the PO and ScMa on quality best practices, and provides quality requirements to the team based on feedback from the PO, industry standards, and best practices (Including performance, security, usability, accessibility etc.).
Developers (DEV) estimate and commit to the estimation on a Sprint basis. They constantly improve the accuracy of the estimation and self-improve from Sprint to Sprint without micromanagement from other roles and managers. Developers distribute between the different expert roles—for example performance, security, and user interface designer.
A Technical Writer (TW) writes supporting documentation for the project. This role can be centralized, since it is usually not required to have a full-time technical writer in the team. However, technical documentation also can be produced by any other role/roles in the team as an additional responsibility."