NO. It's not illegal to have 3 car seats in the back of a car if you need them for your kids.
I used to babysit 3 kids that were under age 4 years old and they all required child car seats by law and never gotten into trouble for having the 3 car seats in the back of the car.
I've been pulled over with all 3 car seats in the back of the car and never was questioned about it.
I couldn't see why it would be illegal to have 3 car seats in the back of the car if your child or children need the car seats.
It would be illegal to not have a child in a child car seat if they required it.
So if your child is of age to need a child car seat and you need 3 of them in the back of the car then you should do so.
You're unlikely to get into any trouble for doing so.
Just make sure the car seats are installed correctly and you should have no issues.