I think it will be hard to give an accurate idea of costs... as it depends so much on what you do, when you get up, when you go to bed etc.
Yes you can take your own food - in fact I suggest you do take you own store cupboard essentials, cereals, anything in fact which isn't frozen or refrigerated. The buy fresh produce on site - such as bread, milk. You can also buy food either on site, or you can get in your car and drive to the nearest supermarket (if at Longleat, there is a Morrisons about 3 miles away).
Your children will need to be accompanied on almost all activities and parents often have to pay... so pick activities that you/dh and your little ones want to do.
Vast majority of your time will probably be spent in the pool - that's free (pound coin for locker, which is returned).
Prices taken from 07.09.2009 Longleat Village Guide. Prices subject to change and may vary from village to village.
There are activities which I feel are best done as Mum/child Dad/child pairs, or as a family. For example... Adventure Golf (9 holes - adult £4.50, child £3.50)
Pedalos - £9 for 30 minutes. Can seat up to 4.
Badminton Court - £8 for 45 minutes. You will need to buy a shuttle cock and hire rackets (don't know costs for those) unless you bring your own.
For your 9 year old and most active out of you/DH - Low Ropes Challenge £15 each. Lasts 2 hours... team building exercise.
Rollerskating Adult: £4.50 Child: £3.50 (size 10+) Adults don't have to pay if not skating.
Bowling £20 for 45 minutes (4 players).
Note: There are sometimes offers on bowling at off-peak (early morning typically) times. If offers are available at the time of your stay, they are usually on a flyer in your villa welcome pack on arrival.
For adults only: Aqua Sana Twilight Spa Session - £26 each, 6pm-9pm.
What sort of activities were you thinking you would be doing?
I would suggest only doing one paid activity per day and you probably wouldn't do one on the Monday or Friday as those are travel days.
If you were to budget for £100 per full day for activities... so £300... I think you could do things within that budget.