Personally, I`d just continue after an activity-filled London (or Paris, or Madrid) layover. Especially in business class.
Book a day room at the Hilton and use the pool/spa/leisure facilities before your flight.
You also will have access to the BA (Galleries Club) and AA (Admirals Club) lounges in T3, both of which have kids' areas with games etc.
I would rather stay overnight in DFW and continue on to COS to break that journey in more palatable chunks. Being spared that late-evening Dallas airport layover and subsequent long-past-bedtime flight will have more of a positive effect on the whole journey than spending a day at a hotel after a short intra-Europe flight.
There's a really nice resort-style Hilton near DFW ("DFW Lakes", just a few minutes on a shuttle) with indoor and outdoor pools that's much nicer than the LHR or DCG offerings (don't know about MAD).