As far as I know, you cannot get the credit as a refund. It can only reduce your tax liability.
You can absolutely get the credit as a refund. The credit cannot reduce your tax liability below zero. However, your tax liability is not what you pay in April. It's the total you owe to the IRS for that tax year, regardless if you over or under withheld. The credit is not available only to people that under-withhold by $7,500 or more. In fact, you owe a penalty if you owe the IRS more than $1,000, so that would be kind of mean.
Check your paystubs and look for "federal tax withheld year to date". If that's more than $10,000 on your last paystub for the year, there's a good chance you are eligible for the full credit.
The form just asks for the VIN. The IRS is not doing any cross-matching to compare the name on the tax return to the name on the title. The only issue would be if your mother gets audited, and they ask for proof -- and you give them the title with her name on it, I don't think they can claim she doesn't own the car.
Agree this is all about an audit. However, it's also about a car that already exists, not one being delivered in the future. So the audit goes like this:
IRS: Show me the title to this Tesla Model X you own
Mom: Here.
IRS: This title dated in 2017? You're claiming credit in 2016.
Mom: Well, we added my name to the title in 2017 so we got a new title after the original one.
IRS. So you weren't on the original title? Well, that's OK. Show me the documents showing it was put in service in 2016 by you.
Mom: Well, I need to get those from my son. (goes and gets) Here they are.
IRS: How come your name isn't on any of the original documents?
Mom: Well, I wasn't planning on having any ownership of this car when my son bought it.
IRS: Well, We'll give you a second pass. It's your car, you drive it all the time, right?
Mom: Well, actually, my son drives it pretty much all the time. It's really his car.
IRS: Well, that's OK, you must have gifted it to him. When you bought it, you drove it home, right?
Mom: Well, he bought it with his own money and drove it home....
IRS: So in what way is this car owned by you, placed into service in 2016 by you, and the use originally started with you?
I don't think this is going to fly. But I don't think it's needed because basically zero people that bought a Tesla as a non-business vehicle have income so low that they have less than $7,500 in tax liability. How did you get $70,000 or $1,500 a month into your bank account without having the income?