The color separation itself is done by the printer. All you'll need to do is send your files properly. You don't need to worry about the lineature and angle but only the resolution (ppi/dpi) of your files.
You should use 300ppi resolution in Photoshop (go in the menu "image" then "image size"). Be careful, the resolution must be 300ppi for the actual printed size of your document; you should see 3x5 and 300ppi in the resolution field. If you see lower than 266ppi or smaller document size, your mom might need to re-do the Photoshop layout again at the right resolution and size.
For your ticket, you'll need to make sure there's bleed applied to it if you have elements that should be printed to the edges (eg. no white borders.)
Add some trim marks to indicate the limits where the ticket will be cut.
Your colors should be in CMYK mode unless you are using a spot color printing process, for example you are using only 1-2 colors on your tickets. If it's printed at small quantity, it's probably on digital press and you simply need to make sure your colors are in CMYK. For this, look at the menu "image" then "mode" in Photoshop and select CMYK.
Yes, Illustrator is better for the text part, and Photoshop is better for the picture or photomontage part. Most designer like to import their work from Photoshop in Illustrator and add their text in Illustrator. You can also use InDesign to import both Illustrator and Photoshop.
Since your mom sent you only a one layer file, you can really re-do the text in Illustrator unless she sends you her real "psd" file with all the layers. It's still acceptable for a ticket to make the text in Photoshop.
I'm assuming you already know a bit about printing and how to use the software but you'll find a lot of details in this site about how to prepare your files!
As final file, you can export your work in PDF or TIFF from Photoshop.
For better quality of your texts:
How to keep the text in vector in Photoshop without rasterizing it or flattening the layers when exporting to PDF?
If you really want to create a color separation (which I don't think you should do yourself), you should do it using the "print" or command, and select the PostScript driver... then select "separation" in the output. You can also do this by "exporting" to PDF and creating a .ps instead. Really, it's usually the printer who does this step, so ask him if you're not certain. You can probably do it in InDesign.
This will create a .ps file that you'll need to drag and drop on Adobe Acrobat Distiller, using the highest print settings. This will produce a PDF with your color separation; it should have 4 pages with black only on each of them.