I will give you some time to realize how pointless it is to create a control like this.
Just for a comparison, I would put a GroupBox on the form and add those 3 mentioned controls to it.
In the Designer, all these can be sized and positioned any way one could desire.
All the properties would be available and I could go about copying and then pasting this GroupBox 50 times if necessary (still preserving the availability of all the properties).
And, for educational purposes, I did bother creating this control so all the members can see one possible way of creating a control that has multiple AHMI controls in it and is exposing all the properties. In the Designer, AHMI controls do have to be sized/positioned manually through properties (if desired).
In order to add any other AHMI control, one would have to follow the pattern in the code and know the layout.
Attached are 2 flavors of the control, Control style which is borderless and Panel style which offers a border (UserControl style was slightly misbehaving and was avoided).
My choice would still be the GroupBox example.