In a page we're designing, we have an issue of there being two tabs (closely positioned) and I wanted some suggestions for alternatives. Essentially in this page, we have a main tab that serves the function of switching between different tables. This function can't be changed but can be displayed differently (drop down wasn't working out). The second tab appears when the user clicks a button on the screen, and a slider opens up into half of the table. In this slider there is another set of tabs. Do you all have any suggestions as to how to maneuver this? Sorry if I'm being unclear, let me know if I can help clarify. I have attached an image for context.
Nothing wrong with tabs
There is nothing wrong with two sets of tabs. Tabs are a commonly used pattern and mostly well understood by people, using something unusual and new might leave users more confused.
From your sketch it looks like you maintain a clear hierarchy, as long as that is maintained in the visual design it should work fine (assuming it's a desktop application).
If you think about it there are many applications that have tabs everywhere. In photoshop, or any adobe product, they are all over the place.
If you still have doubts, test it with people to get some evidence.
Would it be possible to replace the single button with 3 buttons?
If I understood your question correctly, you are talking about nested tab bars, right?
Have you considered placing the main navigation into a sidebar on the left side of the screen? This way, you end up with a menu, that is commonly used and known by users, and also accomplish a clear distinction between your main navigation and your lower-level tabs.
Here are some guidelines that might help you: how to design menus
If you're struggling with the lost space, you could consider hiding your menu behind a burger button, which is another widely used and known mechanism nowadays. However, keep in mind that burger menus could harm the user experience!