Exatly. It's a homemade desing
Engineering is the process of refining a solution to a desired outcomes in light of overlapping constraints. There may be several ways to successfully realise ("make real") a functioning solution to a desired outcome, while avoiding the limits of possible constraints.
One approach may introduce different constraints than another approach, so different approaches may be able to ignore constraints that another approach must provide an answer for.
Your constraints are limits set by aspects outside of your control - the laws of physics, the weight and strength of materials, and also more specific constraints such as your budget, your ability to fabricate or access to someone who can do fabrication for you.
Start by listing the constraints that are obvious to your now. Can you do fabrication? With what materials? Are you in a position to learn some methods you don't know now? It would be a long time from now for me to learn how to weld aluminium in all it's alloys, but I have access to someone that has comprehensive experience, but who also has serious limits on available time.
Will your current wheelchair support this addition? Is it strong enough, stiff enough, does it have frame members that will support the attachment - survey what you have and note your thoughts and concerns to investigate.
Do you know of any other similar system - perhaps one that does not currently have a motor but provides the remaining needs? What is it fabricated from? The material may lend itself to modifications or be difficult to modify - 6061-T6 is strong, but after welding, you must put the entire item into a controlled oven to restore the strength, so you'll need a large, controllable oven.
7005 aluminium can just be left in the corner for a few months and will develop it's own strength, although there are details.
Real things are made of real materials with real dimensions. Can you do it? Sure - many people can, and so probably can you. How long and how much difficulty? You can find out.
Paint us a picture of your situation and the constraints you must accommodate.