How to work authorship of software developed with another University
I don't see the problem here as one of co-authorship, but one of potential plagiarism. That is easy to avoid with proper citation. But it depends, also, on what you intend to do in the papers. 

In a similar case, suppose you found the software and the original papers online or elsewhere and you do some derived work. The originals were done by people who are strangers to you. You cite the original and acknowledge the people who form the foundation. But you don't have to invite the strangers to be co-authors. I don't necessarily see a difference here. 

If they don't participate in the new work they aren't co-authors of it. 

But, it might be worth some effort to try to convince them to participate fully and, thus, become co-authors. 

It would be a different case if you were re-writing the original papers. 

As for the software, you have to be sure that you have an appropriate license to extend it. If you haven't ceded ownership to someone else, then you have joint ownership among the three(?) of you. Get their written permission to extend it, and list everyone as co-authors (co-creators) of the software. But the software and its use are separate things. If you find novel uses of the software without the help of the others, they aren't co-authors of the resulting papers.