If you have any kind of documentation that actually shows your ex is in BC and is intending to stay there and has no interest in his daughter, it would be good to bring that.
For all the judge knows, he's just there for a week and has no idea you are going to court for sole custody. By which I don't mean to suggest you are dishonest, but in court it's better if you don't just claim that something is true, it is better to show that something is true.
From what you describe it's not so much about whether you are Supermom. You don't have to be perfect to have custody. If you have letters backing up what you say about your ex being absent and indifferent, that is better. Heresay (a letter that says "Browneyedgirl has been telling me over and over...") isn't that great a backup, but if a friend or relative was in the room when your ex said he wasn't going to be involved, that is better.
All this probably won't be necessary. If you've served your ex and he hasn't responded and isn't contesting you then you will get custody.
And all that being said, it's no harm to have a parenting plan typed up, or at least some notes about what your plans are for daycare, school, finances, babysitting, etc.
