Access and update class property value from user control C# windows forms

To the extent your goal is not, imho, fully revealed, I am going to show some code that reflects some arbitrary decisions ... in the hope you;ll find the strategy and methods useful :)

I suggest you use a kind of model-view design:

using System.Collections.Generic;
using System.Drawing;

namespace YourNameSpace
{
    public static class Model
    {
        public static Dictionary<UCPlayerAccount, PersonModel> PAcctToPModel =
            new Dictionary<UCPlayerAccount, PersonModel>();
    }

    public class PersonModel
    {
        public PersonModel()
        {
        }

        public PersonModel(int id, string firstName, string lastName, string nickName, int points, int currLevel,
            int currClass, List<Image> avatars)
        {
            Id = id;
            FirstName = firstName;
            LastName = lastName;
            NickName = nickName;
            Points = points;
            CurrLevel = currLevel;
            CurrClass = currClass;
            Avatars = avatars;
        }

        public int Id { get; set; }
        public string FirstName { get; set; }
        public string LastName { get; set; }
        public string NickName { get; set; }
        public int Points { get; set; }
        public int CurrLevel { get; set; }
        public int CurrClass { get; set; }
        public List<Image> Avatars { get; set; } = new List<Image>();

        public string FullName => $"{FirstName} {LastName}";
    }
}

The static Model class maps each instance of the UCPlayerAccount to an instance of the PersonModel Class: the Dictionary values are entered when the UCPlayerAccount is initialized(in the Load Event):

using System;
using System.Drawing;
using System.Windows.Forms;

namespace YourNameSpace
{
    public partial class UCPlayerAccount : UserControl
    {
        public UCPlayerAccount()
        {
            InitializeComponent();
        }

        public PersonModel PModel { set; get; } = new PersonModel();

        private void UCPlayerAccount_Load(object sender, EventArgs e)
        {
            Model.PAcctToPModel.Add(this, PModel);
        }

        // note no external reference is kept to the instance of UCX
        private void btnOpenUCX_Click(object sender, EventArgs e)
        {
            // reference to PModel injected into new instance of UCX
            UCX ucx = new UCX(PModel);

            this.Controls.Add(ucx);
            ucx.Location = new Point(20,100);
        }
    }
}

I am not sure where you wish the UCX to be placed, so I show it here being created, placed, inside the UCPlayerAccount:

using System
using System.Windows.Forms;

namespace YourNameSpace
{
    public partial class UCX : UserControl
    {
        public UCX()
        {
            InitializeComponent();
        }

        // optional constructor
        public UCX(PersonModel pmodel)
        {
            InitializeComponent();
            PModel = pmodel;
        }

        // injected reference
        private PersonModel PModel;

        // test writing to PersonModel
        private void btnWhatever_Click(object sender, EventArgs e)
        {
            if (PModel != null) PModel.Points = 100;
        }
    }
}

Demonstrates how the PersonModel associated with the UCPlayerAccount can be accessed from the UCX.

Since the instance of the UCX is created in the scope of a method in the UCPlayerAccount ... no reference is kept "alive:" ... imho, that is consistent with separation of concerns,

Keeping data models outside Views/Controls pays off, imho, in many ways: for example, the static class 'Model could have a collection of PersonModel that could be serialized, de-serialized, using standard methods.