Just a quick suggestion OP, would you be open to the grandmas looking after your dd2 for a few hours rather than dd1? This would allow you 1 on 1 bonding time with dd1 as well as establish relationships dd2 with her grandmas? I realise dd2 is very young however a short break of 1-2 hours would be wonderful for you, your dd1 will look forward to these times with you, and the grandmas would love all the newborn cuddles!
I have similar anxieties as yourself (ds1 is 2yrs old, ds2 is 10mths) and the only way I've coped has been putting ds1 in daycare twice weekly. I miss him and our relationship dreadfully during these days but I need a break. I'm now transitioning ds2 into daycare and will alternate days between them so I have a balance of 1 on 1 time with each, as well as days when I have both of them. I wish I had a 'village' support network like you do and would certainly utilize the grandmas as much as i could.