WIBTA if I refused to pay for my car being towed?

Last week I tried to drive into work & my car died.

I live at home & pay rent to my parents, I pay for my car/car insurance (on a family plan) & for all of my wants/needs.

My dad works for the car dealership that I purchased my car from & he is a "car guy". He's also a controlling person who always has to be "right."

On sat I turned my car on & when I put it in reverse there was a thunk sound from beneath me & the battery warning light flicked on but the car was still running. I turned the car off & tried to call my dad.

He didn't answer so I went back inside to ask my mom if she knew where the car battery jumper was.

Dad had it with him so she looked at the battery & pointed out the corrosion on the nodes(?) The battery was 2 years old & we live in Florida so things go bad fast & I park outside.

I call into work & called a few auto stores to compare battery prices.

I call my dad again to check if the prices were fair & he tells me don't get a new battery he'll help me clean the corrosion off with a wire brush when he gets home. 

Just go to work (his work is 10 mins south of mine, which is about 25 mins south of home) & if my car won't start when I'm done he'll come jump me.

I was unsure of doing that but my full time job is so crazy busy right now I was feeling guilty not being there so I went with it.

I get on my way & as soon as I tried to go 40mph my car starts to shut down on me.

I manage to keep my head (anxiety issues) & get it into a left hand turn lane before it dies.

I call my dad to update him & ask if I could have it towed to the dealership or if he knew any good garages near by.

He says not to call & he's going to check on a few things.

He's calls back saying he's 10 mins out, don't call insurance.

When he get's there he attaches the battery machine & drives it off the road to a lot & I follow in his car.

He says that he can't see anything wrong except for the corrosion & that he'll drive it home.

Again I say we should call a tow truck.

He says no & like an idiot i listen.

He gets in my car & I ask him to wait for me I'll follow him. He says k & then takes off after I get in his car. I get blocked by incoming traffic and don't see which way he went & he didn't answer his phone so I guessed (wrong) & drove home to not find him.

He finally answered & said he pulled over b/c he was afraid of the engine over heating.

When I reached him he said that that tow was 40 mins out & he was going home to check the aircon. I asked if he had called our insurance & he said "no, someone through the dealership."

He leaves in his car and I wait for the tow.

He comes back as the tow gets there & I find out that the tow cost $200 & he had already put it on his card over the phone.

$200 is a lot of money when I already pay thru my insurance.

WIBTA for not paying my dad back for the tow truck?

It was for my car but he's the one that chose not to call our insurance & arranged for the tow w/o my approval.