Some great points noted.
As mentioned above, your ultimate question has to be - Where would you like to be long term?
If kids are moving schools now, will they potentially have to move again in another few years if they start in Dublin now and then you subsequently move to Tipp?
The availability of school places in addition to finding a property - rental or otherwise in Dublin is not cheap - You are obviously going to get a much bigger and nicer house in Tipp and have a minimal mortgage.
Do you have family support in Tipp? Don't underestimate the value of having this around you.
You mentioned that you recently moved home - Is it safe to assume that this was to be closer to family? Will you be spending your weekends packing the car to head down the country with the kids in tow to see family? As they get older and start more activities, this will get tiresome to them and for you to always be packing and unpacking the car at weekends.
If you all move to Dublin, will you always think 'What if we had moved to Tipp' - Would you realistically consider moving the kids out of school again in another few years separating them from their friends as they are getting older?
The school in Dublin that you have a place for one child in - Are there other schools nearby that you may get the other two into? Your wife will have two school drop offs and two locations for pickups. Would they all prefer to be together in the one school? Realistically, will she be able to return to work and if so, you need to figure in the childcare costs. Realise that it may just be for after school and possibly some time in the morning before school starts, but this does not come cheap compared to down the country.
If me - I would rent in Tipp - get them settled into school. Start your job and think of it as a one year scenario regarding commuting. (Would you have the option to work remotely 1/2 days per week?)
It is always easier to get a job when you have a job. You will know the lie of the land after a few months regarding working back in Ireland and if not sustainable as a long term option, can look for something in Munster with your local experience under your belt.
With your mortgage in Tipp pretty much (or completely) paid, neither of you will need jobs paying large salaries as outgoings will be much less. Undoubtedly living down the country is cheaper than living in Dublin. Depending on where you are living/working in the capital - commute times can be long in any case. Kids can feel rooted in the local community rather than thinking of it as a short term thing.
Use the year to apply for planning and get a feel for the place. If you give it a shot and discover that its not for you, you will have more time on your hands to plan and aim to move all of the family to Dublin next summer, getting their names down for schools well in advance of same.
Its not an easy decision, the very best of luck.