I think you would be best looking at DIY have a look at holiday-rentals.co.uk or holidaylets.net. I have booked an apartment for this summer (Friday for 3 weeks! only £800) using the first mentioned. You actually deal with the owner. You may get something amazing if you could consider a large villa for all of you rather than 2 separate apartments. I think if it for this Christmas you will struggle if you are fussy, we go every christmas and although people are reporting how quiet it has been people are definately there as on new years eve it was rammed even though every other night it was quiet. For flights I use sky scanner which just shows you a list of flights and prices using your criteria. Transfers are easy, taxi at airport or go onto the tenerife forum and ask a question I'm sure someone will come up with something reasonable for you. There is also a map of accomadation on here somewhere, if you want the location you are talking about make sure you are on the shore side of the TF1 or the autopist (motorway).
Hope this helps!