I think this should work for 1and1…to be honest they became more and more a pain in my butt as a registrar and hosting service, so I dropped them about a year ago for almost all of my domains. But anyway, If you’re already paying for DO, you might as well use them as your second name server.
So your first one would be ns1.box.domain.com, your second one would be ns1.digitalocean.com
On the Networking panel at DO, add your domain, set your A record to the IP of the server where you’re hosting MIAB and then add two NS records there, one for ns1.box.domain.com, and one for ns1.digitalocean.com. Go ahead and set your MX records there too, but if you’re letting MIAB do the rest of the DNS, you shouldn’t have to worry about anything else.
Then update that at 1and1 with your two servers and you should be all set.