The rolling open grassland around Brighton, Lewes and Eastbourne isn’t truly indicative of the rest of the SDW. More of the Western bit is on field side bridleways and some is under tree cover. Still pleasant to ride though as long as it isn’t wet and muddy.
If you started from Winchester, stopping at Arundel and Brighton would be nice places to stop and would break the journey up nicely into three days. There will be plenty to see and do while you and your better half are off your bike. Also it’s easy to get between SDW, Town and train station should you need to.
That first stint might be a bit too much though depending how fit you both are. There must be somewhere near South Harting and QECP where you could stop to break that stage up and ride it over 4 days.