Define ´best´-is different for anyone. Cheapest, most comfy, fastest? Also from where? Profile says youre GB, so I assume it can be proposed for sake of easyness from LON? It may also vary if kids are </>10 yet or not. And if you are included as 1 of the parents? Also for about when-that may make huge difference in prices. And also for the chance on strikes on whatever railroad in between.

For train: check on bahn.com what it offers, I saw it possible in 8 hrs (-1 for time difference), via BRUssel, then nasty Thalys-into DE, and in DE fast IC then last part slower regional. For just an out+back return a pass is of no value, but its quite tricky to manipulate fares so that its best for you. On short term this will be quite expensive.

Closest by airport and bigger city is Münster, it has a small airport, shared with next city Osnabrück and lying somewhere in between. Bahn can also give timings. It will have a few flites to at least 1 of LON airports-check yourself. Other nearby ditto small airports are Dortmund. Düsseldorf and possibly also CGN=Köln/Bonn are bigger and these 2 also have stations for direct transfer to connecting train (you will have to change for Emsd somewhere)

In fact being very realistic in this rail-pro forum: probably both fastest, cheapest and most comfy, as no changes, for 4 will be in a car-yours or rental. Either put it on a ferry or on the other €* shuttle-tunnel-train

There is no single answer to that question.  It all depends on how you want to travel, when you want to travel and what your budget is. If you give some more details you will get better replies. 

Indeed. Check Bahn.de. They have a good deal with Eurostar, providing cheaper prices than booking separately via Eurostar. 

Route will most likely be: London-Brussels-Cologne-Emsdetten

I can find prices for 250 EUR, one way, for all passengers for next month. I don't think passes will be good value here, especially if you count the limited pass holder availability on Eurostar. 

So by best, I mean, fun. Kids are good at travelling, we have 7-9 days off over Easter (Friday 7th April to 16th April) for this, the christening is on Easter Sunday. We thought inter rail would be a fun way of arriving, and see some other places, that isn’t just Emsdetten. The kids are (and will still be) 9 and 11 over Easter. We would be coming from London. Thank you so much for all your replies already. 

Then I suggest you make a plan, with timetables (use bahn.com from London) and check pass prices (plus reservations) vs. normal tickets. Also check pass holder seat availability on Eurostar here:

https://www.b-europe.com/EN/Booking/Pass#TravelWish

Note that, as your kids are under 12, they get free interrail passes when bought together with yours, but they still have to pay for reservations, compulsory on the Eurostar.