Answer: Ok, well there's many things that one can do. I'll just give you a simple list but if you ask for elaboration pls let me know on the comments.
1. Delay the party and schedule it on a time that she can come.
2. Send her pictures and letter so that she can see how things really are.
3. Offer to visit to her on a specific time either before or after the birthday party.
4. Asking to bring her mother along in a very comfortable and safe ride so that they can attend the party.
5. Using self-expenses, sending her mother to a hospital where she can be taken care of very sharply or to bring her along and provide her care so that my friend dont constantly worry.
6. You can make party more earlier so that she can visit it and then later afterwards go to the province.
7. Take the harsh way and say, " I am not gonna be friends with you if you dont attend my party!! "
8. Maybe an advicable way that she should visit and take care of her mother because that is more important for her to do. And partys can be done anytime but mother is only once in a whole lifetime.