actually have your director read this
http://www.inmotionhosting.com/support/website/getting-started-guides/unlimited-disk-space-and-bandwidth
IMH Personal & Business Class hosting are shared hosting environments, so to ensure fast & reliable service to all of our clients, accounts that adversely affect server or network performance must correct these issues or will be asked to upgrade to a virtual or dedicated server."
which means as soon as your customer site gets popular and has lots of visits Inmotion may terminate your shared hosting account and force you to use VPS or Dedicated Server.
In other words there is no real unlimited bandwidth free trafic as your director seems to think, because as soon as you cross a line that they have internally defined you will be asked to correct this or forced to upgrade to VPS, so it's better to go with digitalocean.
Their bandwidth for 5$ is 1TB which is probably more then what you will get with shared hosting free traffic with InMotion hosting. And you will probably not sign up to 5$ for your customer but perhaps 20$ which gives you 3 TB.
If you must go with InMotion Hosting email them and ask them what is the real montly limit in GB/TB before they force you to update to VPS. If it's lower then digitalocean or if they do not want to answer that then you should not choose them.