Nameserver strangeness after moving domain

A bit out of my depth at the moment and our DNS registrar isn't much help so far so I'm reaching out for advice here.

On Sunday our company moved our website and email to a new provider, the new provider did everything and appeared to have done a good job.

But now one of the name servers for our domain (our main domain and a mail sub-domain) is alternating between the old IP address and the new one, while the other nameserver is fine an always reporting the new IP address.

If I use nslookup or dig and hit ns1.server-cpanel.com it returns the new IP every time, but if I hit ns2.server-cpanel.com it'll randomly report either the old or the new IP address.

I'll be honest, I'm not even sure who's responsible for providing the information that's being reported by the nameserver, but I'm finding it strange that one of the servers is correct and the other not.

Both the old and the new inftrstructure are still in place, with the old infrastructure hosted by the same mob that does the domains, and they're cpanel managed servers, but from what I can see the old server has had all its DNS settings updated, in the Zone Editor, to point to the new server. I can't see any references to the old IP address anywhere.

It's been a couple of days, so I would've thought any caching should be clear by now, and it seems strange that one NS would be ok but not the other.

Is there anything I can use, or somewhere I can look, that might provide some insight to what might be going on here, could there be something on the two servers that's fighting for superiority?

Or, is this something obviously screwed up at the DNS and we're at the mercy of the registrar? This has been their latest attempt at helping:

I was able to replicate the issue, however, please be reminded that your domain is currently under a shared server and we cannot guarantee that we have a 99% up time. If you feel that our name servers is not reliable you may switch to a different name servers.

Not even sure what the refernce to being under a shared server is about, and needless to say we'll be taking there advice as soon as possible, but in the meantime we need to get our email back up.

Thanks in advance for any advice.