No matter where you have your desk, even if it's in your bedroom, you may still be interrupted by family members asking for things like "a cookie" or "where the car keys are" and so on and so forth. Working at home can be a challenge, requiring a great deal of discipline to get anything done. The difficulty increases when family members interrupt and interfere.
At least partially, you can change this. To protect your office area, you need to install remote control curtains. If you need some time to yourself, take advantage of your remote control and draw the curtains - even if you don't have much space. When you're not deep in thought, you can open the curtains at other times.
After the curtains are installed, your family will respect the boundaries, unless there is an emergency, and allow you to work efficiently so you can be done in time to play catch, watch a movie, or take them out for dinner.
To ensure your wife's satisfaction, you should make sure that the area of the room where you plan to install the curtains is out of the way, won't interfere with the flow of the home, and the curtains chosen match the décor before you hang them. The answer to working in your home office is remote control curtains, so you can find a way to compromise.