3 months notice - difficult managers

[MissDutch]

I handed my notice in yesterday, my bosses were really upset about it.
I thought my last day was going to be the 25th April and informed my new employer. They’ve then said my last day is the 28th and I’m not allowed to work for a new employer until the 29th. I’ve had to email my new employer again confirming this- is it making me look bad? They’re being really difficult and doing everything they can to be a pain. The 28th is a Monday, surely you’d get someone to finish up on a Friday!?
they also emailed all staff this morning to confirm my reasons for leaving and the company I’m moving to. I felt as though this information didn’t really need to be shared. Am I panicking / being a bit dramatic!? Some tips on navigating the next 3 months would be useful.

Honestly I'd just let your new employers know that your old employers are so gutted to lose you they are making you stay to the last possible minute . It will make the new employers look realise how indispensable you are:

What a shame you’re going to be unwell on the 28th

"they also emailed all staff this morning to confirm my reasons for leaving and the company I’m moving to. I felt as though this information didn’t really need to be shared."

And you'd be right - possible GDPR breach methinks?

Launch a grievance on whoever released this info and then leave when YOU want, not when they say - especially if you dont need their reference (or has already been given).

Use this fuck up of theirs to your advantage and leave sooner.