So the school is fine. Don't move. No opportunities to make friends, I find that a little odd. I'm not sure what to make of it. Why would packing up and moving be so much different? I understand if your child is having difficulty making friends... but no opportunity to do so? If the education is fine, then that means you should stay right where you are.
One of the biggest challenges with FIRE is lifestyle inflation. Which is exactly what you are wanting to do. "It's only $250 per month!", "My child may find it easier to make friends" , "Having a 3rd bathroom is really important!"... You can absolutely come up with a million reasons why moving is the right idea.
My suggestion would be to do FIRE math. Meaning, how many more years of employment will this move cost you. Then say "Ok, do I think it's worth working 4 extra years to hit my FIRE goals to have a little bigger house?" Maybe it is. Maybe it isn't. But you aren't going to find a lot of people telling you to move because you want a little bigger house when you seem to already have a house that fits your needs. Don't stress it though. Do what is right for you, but make sure you clearly understand how this effects longer term financial goals. Talking about monthly payment increases and if you can "afford it" is a habit you want to get out of. Don't view things that way.