I want to move my hosting to InMotion from GoDaddy

My Question is:
Now am using another hosting service, But I want to change my hosting provider to inmotion.Okay I will explain you clearly, I have domain in godaddy, mails in inmotion, hosting in wix. Before one week I changed my hosting to godaddy, that time I have problems with my mails, because two providers. Now I fixed that problem.
Now, I have domain and hosting in godaddy, mails in inmotion.Today, I want to change my hosting to inmotion.For this, I have to change my dns name to ns1.inmotionhosting.com, ns2.inmotionhosting.com Am I right.
So I have domain in godaddy, From today, If I change dns, My hosting and mails in inmotion right.
Okay, next, In inmotion I have two plans, One is power plan here I have my mail accounts. For hosting, I bought VPS hosting.
Both are different IP address, For this I have to change anything. Because Before I changed my dns, my mails having problem because two provider, Thats why Im asking you. But these both are in inmotion-one provider, but different IP address.
Please make sure that, mails and website will work fine, If I change my dns.
So in inmotion, I can copy my files in VPS Cpanel. Thats enough right.My mails also working fine, Am I right?
Before one week We faced a lot of problem with mails and mx record and A record.Okay Now I change my dns name to inmotion in godaddy, You can handle all the mails and hosting.Am I right?How long it will take for propagationAfter propagation time My website and mails working from inmotion.During This propagation time, my site also working from godaddy, Please make sure that, It will not go down and my mails also working fine.