Approaching Another Lab With A Project Proposal Based On My Thesis Chapter During my PhD I was stuck on a metabolic engineering problem which I figured out while writing up. I found plenty of evidence for the cause of the problem and devised a complementary system to allow for the desired pathway to function as intended. 

I have had a turbulent but often functional working relationship with my primary supervisor, however, I am quite unpopular with the wider group. After my viva, I had a chat with my supervisor and he wanted to know exactly how the plan worked and how long would it take. Then he suggested I return in a month to explain the idea to a colleague of his who could assess its merit. Now he wont return my emails as I am trying to finalise the meeting. 

Is there an ethics/legal problem with taking the idea to another professor to see if they are interested in having another student complete the work, or does the original university own the rights to the data that the idea was based on?

I suspect some foul play on the part of my advisor, who may want to complete the project without me as an expression of resentment stemming from previous fall outs. I feel like he is trying to plagiarise my work, either that or deliberately trying to prevent it from getting finished out of spite after teasing me with the possibility. Is what I am trying to do plagiarism of his work? Some of the project is based on my second supervisors idea but he got this idea from a paper and just transferred it into another platform. My second supervisor wont accept that my fix is viable, I did first suggest it in my 2nd year of research, but I lacked the evidence. Now I have plenty of evidence to support my idea, it seems watertight and I want to finish it.
Is there an ethics/legal problem with taking the idea to another professor to see if they are interested in having another student complete the work...?


Your current collaborator/PhD supervisor is not returning your emails. This is a signal that work will not proceed. For confirmation, you can outright ask them whether they want to proceed, and inform them that you'll proceed alone if you do not receive a response within a certain window, e.g., two weeks. Assuming you still don't receive a response, you can work with who you want to complete the work. (I'm unsure why another student is being sought. You'll surely need to contribute for any collaboration to be viable.)


  ...or does the original university own the rights to the data that the idea was based on?


With regards rights, you haven't given enough information to answer. If the prior work appears in your thesis, then anyone can continue the work. If the prior work is whatever you conceived whilst employed by the university, then rights will be defined in your contract. If the prior work includes a dataset owned by the university, then permission to use that dataset will be required.