For your budget and based on if I understand you correctly, you have the Pioneer surround sound receiver (with 5 or 7 channels of built in amplification) and speakers and your source equipment already and a expanded budget of $5,000.
You should be looking at a good preamp and a good 2-channel amplifier. Use the center and rear channels of your surround system amplification from the Pioneer receiver and your main two/front channels from the new amplifier.
You have a lot of choices with 2-channel power amps and there are a lot of fairly good 2-channel preamps that will work well within this frame with HT passthrough or Unity Gain. Brands: Aesthetix Calypso (which I have, but factoring in NOS tubes will be too much money for your budget), BAT VK models (I have owned the 5i), Cary models (I owned the SLP 2002 with HT passthrough) and several others. All of these are going to give you very, very good 2-channel performance and not create a problem for your family (assuming all the kids are about 7 or older).
As for a two channel amplifier, again there are many and at very good prices from Krell, Mark Levinson, Classe, Bryston and others.
Avoid buying a 5+ channel amplifier if you are going to use any part of it for a goal of good 2-channel listening. I have owned many from the Dreadnaught II, Krell, Conrad Johnson and others and not a single one could deliver passable 2-channel performance. For the most part, they were all fine for my much lower demanding surround sound needs.
In the end, you should be able to achieve excellent 2-channel performance via this approach well under your budget (assuming the Pioneer is a surround sound receiver and has pre-outs for the front two speakers). $3,500 for used equipment should definately get you were you want to be, including cables.