OP,
Having a husband who is absent a lot means what works for YOU trumps his opinion.
You will be working and at times carrying the whole parenting role.
It's a huge responsibility as any single parent will tell you.
In your situation I would not be moving ANYWHERE that made this load harder.
His parents have zero interest in helping so they don't come into the equation.
Your parents do.
Don't be bullied.
For a couple of years my husband travelled a lot with his job.
With 4 under the age of 8, it was hard and relentless.
Having a support nearby is priceless.
So my advice to you is agree to NOTHING.
Do not say maybe or perhaps as some men will throw that back at you.
Be firm and say No, my parents are a great support to me and I need that support.