Best way to get there...

Start with the assumption that you will return to Europe again. You don't have to see it all in one 12 day trip. Hitting 5 major destinations in less than 2 weeks would be a marathon sprint and would not be fun. I'd recommend taking advantage of your brother's local knowledge and using the trip to primarily explore Ireland. So much to see and experience! If you really must see 1 or 2 more places (not 4!), London and Paris would be easiest. Fly to London and chunnel to Paris. Just remember that travel time eats into your 12 days. But basically I'd suggest that you consider savouring a few places rather than attempting to see them all in a blurr. You will be back.

I know if I tried to visit and visit all 4 of those cities in 12 days, I would be exhausted and feel like I spend most of my time in transit. I would visit and see the sites around your brother, and visit just one of the other city destinations, or at most, two. Any of them would work if you are just doing one so you could pick the one you are most interested in seeing. The easiest would probably be to fly to London. If going to 2 of the other cities, I would probably do London with Paris, or any two of the other three together.

Well you want to visit your brother.. so assume 2 nights.. ( thats only one full day btw) and that you will also be recovering from jet lag that first day or two,, then you mention wanting to see some destinations within Ireland( a whole country) so allow another 3 nights( thats only 2 full days) and now you have 7-8 nights left.
Its pretty ambitious to visit 4 other places in that time. Too ambitious really when you consider each time you move you are using at least 1/2 a day just for transiting.. checking out of hotel, getting to airport or train station,, then transit, then getting to next hotel.
I suggest you look at an "open jaw" or "multi destination " flight.. meaning you fly into one place ( say Dublin) then fly home from another city ( Paris, London or Amsterdam) . May cost a bit more but remember you would have to backtrack to fly back out of same arrival city and that costs too.

I would fly into Dublin,, then take cheapo flight from either Dublin or Belfast to EITHER Paris or London.. then perhaps leave from Amsterdam.. my choices would be Dublin/Belfast to Paris, then train to Amsterdam.. skip London this time as you will have already visited a UK city/country.. ( Ireland) . Even that routing is pushing it as far as I am concerned.. but its doable.

Flying out of Amsterdam or London might be easier then Paris.. no language issues really.

12 days seems like a lot.. but for visiting several COUNTRIES its really a short visit .. take it easy.. its your first time and travel stress is usually related to rushing about .

Here's another suggestion:

For your specific dates, check out where Ryan Air flies direct from Dublin (or any other airport in Ireland) and fly round-trip to wherever the cheap flight is to, for a couple/few days. That way your pick would be determined by what's available... pick one place and this would be easy enough to get away with comfortably, given your time and budget constraints.

You can easily fill a week and more just around Ireland!

For a "quick overview" of the non-Ireland locations, try watching the Rick Steves videos on each city. Then you can choose which, if any, to add to Ireland for this trip. Or which deserve a trip of their own...

628,

since you have 12 days and you want to go to 5 countries/citys, that is approximately 2 days per city not including travel. So you may as well look at it as 1.5 day per city and 0.5 day of travel. just so you know, you will loose one day getting there.

does that sound reasonable to you? If you want an "overview" thats what it is in my opinion.

as far as what to drop is up to you. you know whats more important to you than me.

if it was me, i would spend a couple days in Ireland and 4 days in London and 4 days in Paris. Since they are only a few hours apart by train. but again, its what YOU want to do see.

happy trails.