If no online check in is available then the only way to check in is at the airport.
According to Iceland Air website it is possible to choose seats during the booking process, however there is no info on seat change. It might be possible to change the seat on the website\by calling an agent however the seat you choose is not guaranteed until check in ...
If you must choose such an indirect route then European (2 hours) it is, since you are proposing to leave the UK.
However, as mentioned in Comments, it seems there would be more direct, cheaper and quicker options than flying via AMS.
As an example for June 30, 2017, Flybe offer the following at present, amongst many other options: