It’s definitely a peak train (at Redhill). Being a train the tail end of the peak it is likely to be less busy.
The train comes from Horsham, and calls all shacks to Gatwick before running fast to Redhill. It is overtaken between Gatwick and Croydon by the following train from Horsham which gets to London earlier, and therefore seasoned commuters (and anyone who uses a journey planner) from Horsham, Crawley, and Three Bridges will be the later, quicker train. Similarly, there are plenty of faster options from Gatwick. Therefore the only people likely to be on th train at Redhill will be those from the village stations between Horsham and Crawley, and a few people who prefer the slow train. The train then calls at most stations to East Croydon, and it is for the passengers at these stations that the service is primarily aimed at.
All in, I’d say you will have a very good chance of a seat.
(Caveat, I’m not a regular user of this line!)
The rear first class is declassified, but it is possible that seasoned travellers will have bagged some of them. However the back of the train is never a popular place to sit otherwise, and being at the back is best for exit at Luton airport parkway. Therefore I would wait at the back end of the platform at Redhill, board the second to rear set of doors, look through into the declassified first class and see if there are any seats. If not, then just find a seat in the standard section.
The bus trip from parkway to the airport is a slight faff, but there is a bus at least every 10 minutes at that time of day, and there are a decent number of seats. If the first one is too full, just ask the Marshall if you can be first on the next one. The bus takes 5-10 minutes depending on traffic (which shouldn’t be a problem at that time of day, it’s worst at 0500 in the morning). Easyjet bag drop is more or less the first thing you come to in the departures hall (it’s on the right hand side of the ‘shore line’ as you walk into it) After dropping off your bags go straight through security as the airside facilities are much better than landside. I have never queued more than 10 minutes at security outside peak school summer holiday mornings, and of course there is assistance available if your wife needs it.
