Factors include birth - if you have c section or severe birth injuries then you might not want a next to me right away.
How baby sleeps. You might want to feed then let dh rock baby etc to sleep and burp, do nappy changes.
How dogs respond. I don't know about this, I'm sure there are tips about preparing them but you might need one of you to sleep with them separately.
How breastfeeding goes. Bf is worthwhile but can be incredibly hard. I was put on a schedule where I fed then pumped as dh gave the bottle I pumped after the last feed. Then sterilising pump and bottles. Every three hours, 24 hours a day. Plus nappy changes and burping etc. This kind of thing doesn't lend itself to a shift plan, you just go into survival mode because you can sleep maybe one hour in three if you're lucky.
Really, dh and family wanting to feed baby should be quite far down your list of priorities. You're a mother and baby duo, and that's the main thing in early months. If you decide bottle feeding is right for you then that's fine, but make what's best for you and the baby the deciding factor.
If bf is hard, it's very very easy for family to talk you out of it if there isn't a culture of bf in your family. Again, fine if that's what you want but make sure you're not just talked into it.