This is kind of long. (Sorry), but I work at a place of business where I am the assistant manager. The next door neighbors, and I mean REALLY next door neighbors are being nothing but an aggravating nuisance. They are pulling INTO the EXIT of our business to park close to "their house". And, when they leave, they FREQUENTLY leave through the ENTRANCE of our business.

That is not the suspicious part. As far as I know, there are 2 "elderly" Caucasian women who actually are "renting" the place. However, there is a constant and frequent flow of traffic to the house (through our place of business parking lot) to that house, that ranges from young African Americans, to Mid aged Puerto Ricans, to Older Caucasians. This house gets a WIDE variety of races in and out of the house. Everyone at my work is thinking it's a drug house due to the traffic in and out, I'm starting to think the same, but I have no SOLID proof... just suspicion.

The house itself has been know as a drug house before them. Before them, the tennants up and left suddenly after an investigation, and 1 of the old tennants were arrested in a prostitution ring, and another in a drug bust across town.

Another thing that makes me a bit suspicious, is how much tacky ugly s*** they are putting in their yard to make it "appear" they are not doing anything wrong, but, they are actually just cluttering the yard with tacky, ugly, curb shopping s***!

I feel they are dealing out of the house, or at least have something going on there, and I was wondering what I can do for serious action, seen as the landlord wants to ignore their existence.

I take it that you have given the police a shorter description (leaving out the tacky yard and the races of people) of your suspicions.
The landlord is probably paid in cash and drug dealers aren't going to be late on the rent, so why would he care, unless there is a meth lab about to explode.

So what would I do?
I'd set up a web cam in a window.
I'd post signs about business use only of the lot, and exit and entrance violators will be photographed and reported.
I'd also send a skinny 20 year old out (far side door) next time you see someone leaving on foot or walking towards a car on the street, and have him say 'Hey I only have 10 bucks, can you sell me just $10 worth?' That of course is risky.
Then call the cops again.
Not much else you can do unless you fight fire with fire, outside of the law, but that's not good advice. Just to let off steam.

Is this a residential area or mixed use? Is your business a commercial building or run out of a house? Do the owners of the business own the property or rent?

The easiest thing might be to put up a fence around your property to prevent using your driveways. I would check with the local building dept to see what the rules are using a driveway, They may not be doing anything illegal that they could be ticketed for.

As for reporting a possible drug house, I would be careful about making racial remarks. Simply tell the police there is a lot of traffic in and out of the house and that they use your driveways in the wrong direction.

I would certainly put up fake surveillance cameras, if that doesn't help then make them real.

As for as the drug sales, are the visitors staying 10 minutes or 1 hour ? May change my opinion of what is happening. Also, I may not send someone there, if perhaps, it is a undercover police operation, the person you sent, is not guilty of buying drugs.

How is it, of course hurting your business? Is the parking a real issue? Has the manager went over and talked to them about not using your parking lot?

Has anyone complained to the police? To Zoning about the yard?

Is there signs in parking lot, "for customers only, all others will be towed" and check local laws and start towing some cars. Put up a fence, so people can not just walk to house next door. Put up security cameras.

...
As for reporting a possible drug house, I would be careful about making racial remarks. ...

The OP does appear to be stereotyping; the racial characteristics of the suspicious people don't matter to us, but they may be helpful to the police (for the purpose of identifying suspects).