As I said, you may have to fight very hard to ensure your rights are protected. We were lucky: we had a close friend with many years’ experience as a HR director who advised us. We also got advice from a lawyer specialising in the area (not cheap!). An alternative is to get support from a union (despite all the anti-union rhetoric that's out there, they can be a huge support in cases like this).
They sound like an employer you wouldn't want to be with in other circumstances. Given that, my advice would be to transfer over (if you leave, you loose any rights), assert yourself to ensure your T&C are met (and they don't expire after a time), document anything you feel is not right at the time it happens in case the worst happens and you do have to take a case, and start looking for a new job.
It can be very debilitating working for somebody who are determined to ensure you are "dealt with" at the lowest cost, regardless of what that means (in our case this included not paying full salary and then an unfair dismissal). I cannot understand companies like this: in my experience companies who deal with their employees in a fair way are invariably better from a business perspective than those who don't. It sounds like you may be dealing with one of these: hence the advice to get out.
One piece of advice we had was that if it does start to go bad, try and stick it out and address matters without resigning: constructive dismissal claims are harder to take and prove than other types of claim.
Make sure you're well informed: use Google for "Transfer of Undetakings Ireland" for more information and advice.
Good luck!