Thanks for the further information - again, I'm not providing legal advice, just my interpretation.
Will you get in trouble for using the recording? Legally, no, you won't be penalised, but the judge is unlikely to consider it in his decision unless the grandparents are made available for cross-examination.
So far, you have done well by negotiating an outcome outside of court, but family law is as much about perceptions as anything else, so some things to consider...
First, going through court for 50/50 as opposed to 44/66, or one extra night of care per fortnight, runs the risk of hurting your case because I think it's going to be difficult to show that one extra night with you is better for the kids than the stress of a long court procedure and the legal conflict with the mother that you will be prolonging by pursuing that extra night.
What does impact the kids' best interests, however, is the fact that they're missing school and living in a three-bedroom house with up to seven people at any given time. Are you better equipped to get them to school every day? Is your living situation more stable and consistent?
Judges don't care for mud-slinging matches between warring parents, they only care about the best interests of the child. I wouldn't go in telling the judge what a terrible person the mother is - after all, you also need to show that you can encourage a meaningful relationship between the mother and kids if they were to change residences. I would go in telling the judge what your concerns about the kids are and why you think it's in their best interests to live with you.
Just be warned, though, that going for a change in residence is a very, very difficult path, and an often unsuccessful one. Speak to a solicitor to get a better idea of how to pitch your case.