Two people form a research partnership to investigate a specific research question. Person A comes up with the question draws up a plan. Person B joins and advises on the approach and assists in data collection (a significant enough contribution to be a co-author). They both run the analysis together but have a difference of opinion on how to write up the study. They can't agree and the research partnership dissolves. Person A and Person B both want to pursue the question independently using the data they jointly collected but neither will consent to the other submitting first. Does the research question and data dissolve with the partnership or is there a way forward I can't see?
In as much as you are asking about "ideas", no one owns them and anyone is free to follow up on them.
But if you are asking about who owns the product of joint work, work worth of authorship, then everyone contributing IP has a stake and that stake can't be claimed by others. If you can't come to any agreement, then you are stuck and anyone can potentially prevent publication or force a withdrawal. So, your best option, if you want to continue, is to come to some accommodation.
It is, however, possible in principle to start over, discarding all previous work, based only on ideas. That is risky, however, as it is difficult to do it "cleanly" without generating complaints from others.