AIBU - feeling you can't just take baby for a drive hours away for a weekend without negotiating with your partner, the baby's dad - yes YABU.
"- feel like I have to ask permission to make plans on weekends and evenings because baby is ebf and again I feel bad that DP won't see him those days."
I think you never need to ask permission for yourself but as a family now you probably do need to negotiate time and places and who is doing what and when because you are now a family in a special way and baby comes with you which might mean dad gets pushed out.
"He's not objecting to me going completely but wants me to go in the week when he's working (when my family are all working too so what's the point in me going?)"
Presumably your family are not all working 24/7. If you are at home with baby all the time and your dp is working and your family is working I would negotiate things between you all.
It is important your dp gets to bond well with baby. If the situation were reversed and my dp were at home with baby all week and then took baby to see family at weekend when I was at home I would feel very upset.
I am not saying I agree with him about everything but in this area I think you need to work things out so your dp gets to see the baby plenty too, and does his share of child care etc.
Going to family without baby's dad potentially every other weekend will become, I think, very disruptive to family life in the long run.
"Really frustrating..." If I were your dp I would equally find this Really frustrating...
Just as an aside when my dad died I was pregnant. Our early life with dd was spent going to my mum's house a lot. My dh accepted it because he knew I wanted to help my mum and also my dh came too. And it was not four hours away. But it did mean in those early years are family life was not great and I do have a new sense of pride that my dh supported me so much.
Returnofthesmileybar "Go home to your family, you need time with them too and don't ask or apologise, discuss by all means, but don't ask!"
But the OP is talking about a visit home potentially every other weekend, presumably for overnight, perhaps even more than one night. Would you be OK if your partner took your new baby to their family every other weekend when you were at work all week? I'd say even once a month is a lot.