The Cotswolds are a rural area that's not so easy to visit without a rental car. There is precisely one train station in the Cotswolds (Moreton-in-Marsh). Buses fan out from there, but it can be difficult to visit very many small Cotswold villages in one day by using public buses. And the villages are rather small, so you probably don't want to spend the whole day in just one or two of them. I assume there are some taxis in the area, but I never investigated that possibility and have no idea what it might cost to get around for a day by taxi, and how much waiting that would entail.
I opted to take a one-day van tour. There are tours running out of Bath (MadMax, maybe others) and Moreton-in-Marsh (GoCotswolds, maybe others). Moreton is a short train ride from Oxford, which is a very interesting city in its own right, so I stayed in Oxford and caught an early train to Moreton to join my tour. I see that GoCotswolds charges 110 GBP for a family of 2 adults and 2 children, which strikes me as a very good price, indeed. Other tour companies may offer similar deals.
Some of your other targets may also be visitable from Oxford; I haven't been to any of them. One advantage of doing some of your day-tripping from Oxford is that you'll probably find your lodging expense to be lower there. London hotel rooms tend to be tiny or expensive. Or both.
I'm sure Ireland is lovely (haven't yet been there myself), but I suggest that you begin exploring your transportation options now, before you get committed to including it. Be sure you can get reasonably-priced, convenient flights for the days you will want. I think any alternative (train + ferry) would cost you way too much of your precious vacation time.
It sounds like you've already bought roundtrip tickets to London. You might have been able to buy multi-city tickets that allowed you to fly into Dublin and out of London (or vice versa) for the same price.
