I don’t think the OP was merely asking about ALL manner of work on Sundays. OP just inquired as to whether what OP’s actions were improper.
Making purchases that are not immediately necessary to life can wait for another day. Purchases of food or medicine are acceptable on Sundays as they serve to sustain life.
OP – you are the minority in your family, so you will inevitably meet with obstacles. You were respectful towards your family and explained your reasoning which is perfectly acceptable.
Making it clear that you will gladly purchase the grill on a weekday will show your family that you are not trying to be difficult, or holier than thou, or unrealistic.
The 3rd Commandment applies to unnecessary servile work. It’ doesn’t obviously include those in the medical field, police officers, firefighters, etc.
It does however apply to those who choose to do leisure things instead of giving proper worship to God where they miss Sunday Mass because of it. Maintaining the cleanliness of the house and cooking are acceptable. To reserve specific manual projects (ie.: painting the house or cleaning the gutters, etc.) to do on Sunday is not acceptable as God created the Sabbath for man and not man for the Sabbath. He LOVES us and wants us to rest and use the other days for work.
Now, with that said, I don’t know your age and I don’t know if you are still subject to your parents’ rules. If you are underage (younger than 18), which I assume you are as you are “practicing” driving, then picking up the grill may have been under the requirements to obey your parents. Honoring thy father and mother requires you to obey them as a child living under their roof provided they are not demanding you to commit an aggregious sin. You would be obeying their request and not simply choosing to shop on Sunday because ***you ***wanted to.
Sometimes obedience to our superiors is more acceptable to God than is our own will.