Any vehicle that is parked and garaged at your address needs to be insured for that location. Car insurance companies use your address and zip code as a risk factor.
There isn't a consent form. What I would recommend is contacting the insurance company and advising them of the situation to see what they can do to remove you from the policy.
Coverage & Claims
Yes, as long as she is listed as a driver on the policy, she can stay on her ex-husband's insurance policy. With that being said, it is no longer the ex-husband's responsibility to carry insurance on the car.
If he is taking out an insurance policy in your name simply to get a cheaper rate, he is committing insurance fraud. What I recommend is contacting the insurance company your husband is attempting to use and letting them know you are not on the policy and that you two are separated.
If they are still legally married, she would need to be listed on the policy. But, if she's not using the vehicles or doesn't own them, she can be listed as an "excluded driver" and thus your policy won't be affected.
Generally speaking, that shouldn't be an issue for your homeowners insurance company. For the sake of avoiding any sort of confusion down the road, however, it may be beneficial to update your existing accounts with your mortgage provider.
Generally speaking, the parent with primary custody should insure the child on their policy. The tricky part would be if your son will be driving your vehicle while at your home and his father's vehicle when he stays with him.