Hey y'all! I've been trying to find answers online but no dice - hope this isn't a silly question but I'm so lost and going around in circles.

I'm working with print/CMYK for the first time in a WHILE, especially where the brand colors are so important to get accurate. The last time we printed menus with this printer, the colors came out darker/yellower than expected despite me designing in CMYK, so the printer said to send them exact CMYK values to match.

I clicked into the color picker of the goal color - Hex #DD566D. The CYMK value says 0,87,42,0. I double checked it in a CMYK to Hex converter thing and that CMYK value showed up as SUPER hot pink - definitely not the goal. So I did the opposite: I took the Hex color into a Hex to CMYK converter, and the color on the screen looked correct, but the CMYK values it gave me were 0,53,44,13 and that's super muddy orange??? I've attached examples of all of this.

I feel like I'm going insane lol and I have to get these to print asap. I know Hex to CMYK conversions aren't 1:1, but I have no idea what to send the printer. Unfortunately I don't have any kind of physical swatches to use, and this isn't the first time Illustrator in CYMK mode has been pretty off from screen to PDF to print. In fact, the switch from RGB to CMYK doesn't show a visible difference and I have no clue how to fix it. FWIW, the PDF looks accurate enough when saved out.

Any tips on how to get Illustrator to show a more accurate color, and any tips on how on earth to get the color I'm looking to achieve? Thanks in advance!!

Edit: Unfortunately I don't have access to a Pantone book. I've been looking online to find the closest Pantone color to the one I need, in hopes the printers can at least use that as a jumping off point. I found a nearly perfect one, but the CMYK values given for that Pantone swatch still look DRASTICALLY different in my illustrator file - it's super orange comparatively. Is this an issue with my Illustrator or am I missing something lol