I've just taken a look at the rail fares. (NB: I've assumed that Bridge of Allan is your nearest station)
I assume that you've got a Family & Friends Railcard. If not, you definitely need one. £28 for a year's discounted travel (or £25.20 if you but online before the end of the year):
http://www.familyandf...railcard.co.uk/online
To maximise your time in London you could catch the 0710 train from Bridge of Allan on 15/02. That gets to Edinburgh at 0817, leaving you just 13 minutes to wait before the 0830 departure to Kings Cross (arriving at 1254 and thus giving you the afternoon and evening to explore London). The total one-way fare (for 2 adults & 2 children, with a Railcard) is currently £50.10.
(That fare is also available at 0801, getting into Kings Cross at 1355)
However leaving a little later takes the total fare down to £32.50. (The 0831 service gets to Edinburgh at 0932, with the 1000 connection to Kings Cross arriving at 1446).
To maximise your time in London on 17/02 you could take the 1700 service from Kings Cross, arriving in Edinburgh at 2127. However you've then got an hour's wait for the 2233 service to Bridge of Allan, arriving at 2329. The total one-way fare is £81.60. (The 1600 and 1630 services are also available for the same fare, with better connections at Edinburgh).
For economy you could take the 1300 service for £63.80. (Arrives Edinburgh 1725, with the 1801 service to Bridge of Allan arriving at 1859).
So you could do the return trip for around £100 (for all four of you) but another £30 or so gives you more time in London.
http://www.nationalrail.co.uk/
(Remember that 'Advance' fares can go up dramatically - or simply become unavailable - as the date of travel approaches. I recommend booking a.s.a.p.).
Chris