The good thing about the 'offer to leave' is that that shows a will to dismiss, which is unfair, and could also be taken as an inducement to resign, which again indicates a will to constructively dismiss, and could be a good position to negotiate a midway between what a constructive dismissal payout would be. You have to make a reasonable attempt to find alternative work for this to illustrate you have been disadvantaged. If you are unable, or its realistic that new roles would only start in September, and especially if you secure a position that does, then your disadvantage would be paid until end of August anyway, and their 'win' is that they save the legal costs too.
You may be able to withdraw your resignation and ask for investigation of the disciplinary issues, which will take until end of August at least as lots of paperwork will need to be shared and investigated, meetings scheduled, witnesses called etc. You wouldn't be unreasonable to expect suspension on full pay during investigation.
I do know that the trick is to ask them for all the info and complaints they have and stay silent until they have given you everything (apart from perhaps negotiation options) so that a. You can prepare responses and b. So they can't add evidence later. One of my employers faked and added evidence, which made them look like utter arses at tribunal.
Get lots of advice, you don't have to follow it, or appoint, but I got initial advice from several sources, but used only the union for formal advice and representation. Just don't tell them, or have non union legal people communicate with employer.
Also keep it as an intellectual exercise and as simple as possible, and allocate specific days to new employment search too.