Your preferred option will be disruptive for your children at this crucial stage in their education and in their friendships. You will all be vulnerable moving into another person's home should the relationship not survive living together as a family.
The option of staying with their clearly selfish and useless dad does not appeal to them. They would hate it along with seeing their mother abandon them.
The option of staying with your grandmother might be their preference but it is unfair to dump then on her so you can move in with your partner. Your grandmother is an older lady looking after teenagers solo would be a challenge. And your children would still be seeing their mother abandon them. And your grandmother is also dropped by you like a hot potato.
The option of your partner moving in is also unacceptable. She would have to sell her home and resign from a secure well paid job. that's her security and I wouldn't be surprised if she's unwilling to sacrifice that the off chance the relationship works out. What happens if she can't find a suitable job near you? What happens if the relationship cannot withstand the pressures of your children perceiving that someone who is basically a stranger has been put into their home, their sanctuary. What happens if she finds it tough living with your children! Even parents can find their own teens tough work, just look at the threads on this site. She'd be the one that would obviously leave having sacrificed her previous home and work.
It strikes me that everyone loses out in the various options listed above. Apart from you. Because you get what you want without making the sacrifices your children, your grandmother or your partner would make. It's usually the parents who make sacrifices for their growing children. Yup your ex is a twat. But you have to be there for your children. And you need to recognise that every one is best served by you staying where you are and your partner staying where she is until your children have become adults.
Keep it as a romantic relationship without living together. Long distance relationships can work out, and if it does so over the next few years then It's got a good chance of withstanding the inevitable change and challenges of living together in the future. Long distance relationships are hard work but can be very successful.
If they fail then its likely that living together would have also been a disaster because that brings its own stresses and strains on a relationship. And if it fails at least neither partner has had to uproot their lives and their responsibilities. It's better for all.