Ok I think a few things need to be made clear first 1 do you both have a ps4 or is it on that you both share.
2 Do you both share the same account and also save data is sepret from psn account that's just the profile save fames are sepret from this.

3 it also sounds like your having a connection problem the ps4 WiFi is kinda weak for this game what you want if this is the problem is to either have it hard wired if you can or get a stronger router the stronger router and having the ps4 be the first thing it detects will give it priority on it in connectivity this solved my problem when I had to use the WiFi.