Your tree looks very healthy. The depression between the trunks looks amazingly clean and dry! Keep on doing what you are doing because it is working.
I see that your neighbor to the west has an even larger tree. Have you talked with your neighbors/friends who have these mature oaks next to their home what they have done and how often these trees break big limbs?
The good thing about oaks is they have tough wood and branches are more horizontally attached. A larger angle is stronger than narrower angles of branches to trunks. These trees are the best to have if you've got large trees planted close to your home. They don't break easily.
The information I need to know would be 'what is the usual direction of the wind'? If it is from the south, I would not worry at all. Still, for insurance purposes call the closest Cooperative Extension Service and get a reference for a bona fide arborist (check their licenses and certifications).
They'll look at the health of your tree, recommend certain branches to be removed or none, discuss getting a soil sample tested to see what chemicals/fertilizers are deficient/in excess.
Some homeowner's insurance policies might have stipulations such as requiring large trees near the home to be diagnosed by an Arborist before they will insure the home for tree damage.
Upon a bit more circumspection of that girdling root, you should saw that off 1/2 inch from where it is connected to the trunk. Saw the other end off at the surface of the soil and remove this root/branch away from the bark of this tree. Where it is touching it is causing moisture to stay way too long and bacteria will eventually ruin that part of that trunk's vascular system. The arborist will be able to verify this necessary surgery, I am sure. I am sorry, I thought I had addressed this great example of a 'girdling root' allowed to continue growing. I am keeping this picture for visual aids...!!