EBF baby/going out or letting people babysit

Hi guys, ima ftm and my son will be 12 weeks this Wednesday and he’s EBF— I’m the very first in my family to breastfeed and I have a goal of making it to atleast a year! Anyways, we are moving to my home town this week and my family wanted to take him for the day so we can move. However I’m not comfortable w that bc one he’s still little, and two, since he’s EBF he feeds on demand. Ive already been criticized in the past when we would go home (he was 3 weeks old) and I would wake him to eat after he’d been napping 3 hours among other things. my family doesn’t understand how breastfeeding works- and I’m gonna tell them no to taking him for the day bc I’m not trying to mess w my supply/have to pump while moving and also I’m just not comfortable w it and I already have a feeling my family is going to give me crap for it and I’m honestly over it- I’m not wrong to be like this am I? He’s just so young also lol like I appreciate the favor of watching him, but I’m not ready for that, and he isn’t either- they don’t understand what I’m demand feeding is. Someone have advice? Am I crazy for feeling this way? How do u other mamas do it? TIA