 Here is a simplified Python code that follows your instructions. Note that you need to have Fealpy and SciPy installed. Also, the exact solution and the CosSinData function are not provided in this code.

```python
import argparse
import fealpy as fp
import numpy as np
from scipy.sparse.linalg import spsolve

def curl_curl_solution(u):
    # Define the curl_curl operator
    # This function should be implemented according to your specific problem
    pass

def least_squares_matrix(u, cell):
    # Define the least squares matrix for each node of a mesh
    # This function should be implemented according to your specific problem
    pass

parser = argparse.ArgumentParser()
parser.add_argument('--degree', type=int, default=2)
parser.add_argument('--h0', type=float, default=0.1)
parser.add_argument('--max_iters', type=int, default=5)
parser.add_argument('--theta', type=float, default=0.5)
args = parser.parse_args()

problem = fp.CosSinData(degree=args.degree)
mesh = fp.MeshFactory.create_box_mesh([0, 1], [0, 1], h0=args.h0)
mesh.remove_subdomain(4)

for _ in range(args.max_iters):
    V = fp.FirstKindNedelecFiniteElementSpace2d(mesh, degree=args.degree)
    u_h = fp.Function(V)
    bc = fp.DirichletBC(V, problem.exact_solution, fp.Function(V.sub(0)))
    a = problem.form_a(u_h, bc)
    f = problem.form_f(u_h, bc)
    K = a.matrix
    b = a.vector
    b.axpy(1, f)
    u_h_sol = spsolve(K, b)

    L2_error = fp.norm(problem.exact_solution - u_h_sol)
    curl_error = fp.norm(curl_solution(problem.exact_solution) - curl_solution(u_h_sol))
    recovered_curl_error = fp.norm(curl_solution(u_h_sol) - curl_curl_solution(u_h_sol))

    if _ != args.max_iters - 1:
        markers = np.where(recovered_curl_error > args.theta * L2_error, 1, 0)
        mesh.refine(markers)

fp.showmultirate(L2_error, recovered_curl_error)
```

This code is a starting point and may need adjustments according to your specific problem and the exact solution you are working with.