student visit visa + dependents

[insidematrix]

Hi,
I will be applying for student visit visa to attend a 2-week residency for my online studies.
I understand that my dependents (wife+infant son) cannot join me with the student visit visa.
I want to have a 3 week stay, attend the 2 week residency and spend 1 week with my family for enjoyment.
I will have a 3 week family hotel booking + to & fro ticket booking for entire family + train tickets and cash / credit cards for food and travel expenses for my 3 week stay.

My question is that how my family (wife + infant son) will join me? if as a general visitor then what are the chances for them getting the visa to accompany me?

For budgetary purpose, can somebody give me an idea on how much money is required for 3 week stay in UK (country side) with family (3 memebers, myself , wife and infant son) which includes 3 times food + some taxi charges and something to spend on leisure.

Thanks.