My puppy cries when I leave. How to stop puppy separation anxiety?

Sounds like some separation anxiety is starting. You should try and keep her distracted while your mother prepares to leave. Dogs will pick up cues like putting on shoes or picking up keys and start to feel anxious. Sometimes just doing these things and then not leaving will help, as the dog will start to disassociate that with her absence.

Also practice getting your mom to leave for very short periods of time and keeping the dog busy in the house with a food dispensing toy, play time etc. Or just chilling quietly and rewarding her like crazy when she isn't looking to the door, acting anxious, whining etc. Have your mom come back. Any time she leaves or returns she needs to not make a big deal about it for the dog. That means no more "Ohh Fluffy, I'm so sorry I''m leaving" or "Hiiiiii Fluffy, I'm home, oh, aren't you just the best dog ever?!". It needs to be really neutral so they dogs behavior isn't being reinforced. Any attention (good or bad) is attention to the dog and you can actually be rewarding them for doing things you don't want reinforced by accident. Keep working on building up the length of time that she is gone and the dog is comfortable.

You are absolutely correct that the sooner you get started on this the better off you will be!

I also recommend upping your dogs exercise. A tired dog, is a good dog. Dogs with extra pent up energy are more likely to find ways to keep themselves busy and this usually means by doing something we won't approve of. Most "bad behavior" is stemmed from pent up energy and frustrations, and is just a way of expelling that. Make sure walks are just not a leisurely stroll. They need to include running, jumping, sniffing around, try some commands-anything to get their mind and body working together, and tired.

If you aren't able to work through this yourself you will need professional help and guidance to work through this issue and give you the tools to be effective in helping her through this. This is imperative that be it addressed now. Over time, the behavior re-enforces itself and it gets worse and harder to treat.