Is it possible to have two partial classes in different assemblies represent the same class?

No, you cannot have two partial classes referring to the same class in two different assemblies (projects). Once the assembly is compiled, the meta-data is baked in, and your classes are no longer partial. Partial classes allows you to split the definition of the same class into two files.

As noted, partial classes is a compile-time phenomenon, not runtime. Classes in assemblies are by definition complete.

In MVC terms, you want to keep view code separate from model code, yet enable certain kinds of UI based on model properties. Check out Martin Fowler's excellent overview of the different flavours of MVC, MVP and whatnot: you'll find design ideas aplenty. I suppose you could also use Dependency Injection to tell the UI what kind of controls are viable for individual entities and attributes.

Your aim of separating concerns is great; but partial classes were intended to address entirely different issues (primarily with code generation and design-time modelling languages).

Extension methods and ViewModels are the standard way to extend data-layer objects in the frontend like this:

Data Layer (class library, Person.cs):

namespace MyProject.Data.BusinessObjects
{
  public class Person
  {
    public string Name {get; set;}
    public string Surname {get; set;}
    public string Details {get; set;}
  }
}

Display Layer (web application) PersonExtensions.cs:

using Data.BusinessObjects
namespace MyProject.Admin.Extensions
{
  public static class PersonExtensions
  {
    public static HtmlString GetFormattedName(this Person person)
    {
       return new HtmlString(person.Name + " <b>" + person.Surname</b>);
    }
  }
}

ViewModel (for extended view-specific data):

using Data.BusinessObjects
namespace MyProject.Admin.ViewModels
{
  public static class PersonViewModel
  {
    public Person Data {get; set;}
    public Dictionary<string,string> MetaData {get; set;}

    [UIHint("FCKeditor")]
    public object PersonDetails { get { return Data.Details; } set {Data.Details = value;} }
  }
}

Controller PersonController.cs:

public ActionMethod Person(int id)
{
  var model = new PersonViewModel();
  model.Data = MyDataProvider.GetPersonById(id);
  model.MetaData = MyDataProvider.GetPersonMetaData(id);

  return View(model);
}

View, Person.cshtml:

@using MyProject.Admin.Extensions

<h1>@Model.Data.GetFormattedName()</h1>
<img src="~/Images/People/image_@(Model.MetaData["image"]).png" >
<ul>
  <li>@Model.MetaData["comments"]</li>
  <li>@Model.MetaData["employer_comments"]</li>
</ul>
@Html.EditorFor(m => m.PersonDetails)