This has been covered in some of the other threads, but I will repeat it here.
Applying for a British "EEA family permit" is quite straight forward. As long as you are not illegally in Ireland, which it sounds like you are not, and you are (e.g.) married to an EU citizen, you should have absolutely no problem. You do not need to have a specific long-term status in Ireland, such as a Residence Card.
Apply now for a weekend away in the UK. After your weekend, you should send evidence of your few days residence in the UK to the Irish government to indicate you have resided in another EU state.
If you decide to leave Ireland, it is the same application. If you want to be resident in the UK for more than 3 months, you (or more easily your EU spouse) has to intend to look for work or have work already arranged work. But the family permit will be issued just as easily.