convertible car seat question

Samantha • 💍💕👨‍👩‍👧‍👦
My daughter is just about 4mo and I decided to buy a convertible car seat. She hated every time she was in her infant seat bc she always wants to sit up so I thought this was a good investment. Soon I'll see if she just hates car seats period. But anyways, in the mean time, I'm curious what you mamas do with baby when you go to store or out to eat, etc. where do you put baby since you can't just pick up the seat and go?? I have a Carrier so I think I would use that when shopping or a quick run somewhere. I also have a stroller but it's rather large bc it is one you can have the car seat on it too.  Should I buy a smaller light weight one?