Jami,
I have to agree with Frank. I'd also skip Greece this trip especially with only 21 days to work with. As this is your first trip to Europe, definitely add a few days to both London and Paris (and perhaps Munich if you plan on day trips). IMO, you'll have a far more enjoyable trip with a more relaxed Itinerary rather than rushing about. As someone else mentioned, keep Rick's advice in mind - "assume you will return".
It would help to know which locations in Ireland you plan to visit? Are you planning on spending 5 days just in Dublin or taking a few day trips as well? Remember that you'll lose the first day in flight times and time zone changes, so your trip will actually be 20 days (also, don't underestimate jet lag). You'll have to allow for travel times also, especially between Paris - Gimmelwald and Gimmelwald - Munich.
I'm assuming you've read Europe Through The Back Door so you'll be up to speed on rail skills, etc.
Under the circumstances, I'd probably arrange things along these lines:
Day 1 - Fly to Dublin
Day 2-4 - Ireland
Day 5 (morning) - fly to London (check RyanAir or EasyJet and be sure to PACK LIGHT as the budgets are brutal with baggage limits).
Day 5-8 - London
Day 9 (morning) - EuroStar to Paris (from London St. Pancras)
Day 9-12 - Paris and day trips (Versailles?)
Day 13 (morning) - TGV / Train to Interlaken and Gimmelwald (this will take ~5-6 hours and several changes)
Day 13 (afternoon)-16 - Gimmelwald, Schilthorn, Murren, etc.
Day 17 (morning) - Train to Munich (this will also probably involve changes, but I haven't checked)
Day 17 (afternoon)-Day 20 - Munich & day trips (Castles, etc. - I used Radius Tours for that trip and it was great).
Day 21 - fly home from Munich (use the S-8 to get to the airport - very easy)
There are lots of possibilities, but this Itinerary would be reasonably "relaxed".
Good luck with your planning and happy travels!