We're almost ready to exchange contracts in a 4 part chain and I'm 8 months pregnant. One of the chain want completion ASAP, we want ASAP but our buyers have picked 26th sept as their preferred date, their buyers are flexible. I'm 39weeks on 26th so obviously want to move before that but they seem quite inflexible about sooner. Our EA isn't being sympathetic and seems to have taken their side. I've asked if there's a reason and was told by EA that's the date they've discussed with removals firm 
How should we go about negotiating? Who has the most power in discussions, is it the solicitors or the EAs?
Any advice would be greatly appreciated as I'm getting a little stressed and exasperated that one person can seemingly pluck a date out of thin air to suit themselves but no one else's situations seem to count.