@Rodrigo_Souza, I don't have any answer to your concerns, but I do have a checklist of things that have changed when migrating servers, so here are a few things to consider as you troubleshoot.
That's a big flag for me. I don't fully understand what you mean there, but there are various configurations with mirroring that can mess up analytics. For instance, if you moved over just one domain, and left the other in place, are you checking analytics for it? Is traffic going there, instead of the one you want?
Don't be too worried about that! I am just listing out possible ways your traffic isn't being registered.
And finally, how well do you know your traffic? Looking at it historically, is there a particular source that generates a lot of traffic? Has your visitor engagement changed? I ask, because if I suspected DreamHost was involved in the dip, it would be at the "firewall" level. Sometimes a site gets a lot of bot traffic, and hosting providers can block it for quality of service reasons. Again, don't worry about that! If this is the case you'll figure it out looking at your historical data, and can bring that up with support. And it probably doesn't account for the dips you are seeing; I presume you weren't getting 50,000 hits from bots.
These are just ideas to help you think about what changed. I listed them in the order to think about.