This is my First Post on Flyertalk!

I have not traveled internationally in over 15 years. Going to Dubai in May. Most routes from Denver go through London or Amsterdam. Wife and I would like to add a 3 or 4 day layover in one of those cities on the return trip. It appears that this adds about $1,000 to the price even with the same flight home. Are there secrets for getting reasonable layover deals on these long flights?