Yes, 6 weeks will require a fair bit of money and a few hundred baht a night will make a big difference over 6 weeks.

A budget hotel or guesthouse might suit your needs.
While there are plenty of these in Bangkok and Kanchanaburi, an apartment may still work out cheaper, depending on number of people and the sleeping arrangements.

So, if you provide a few more details, perhaps someone can make some recommendations.
Apart from yourself and 2 kids, who is in your group? Couples or singles? Total number?
Do you have an idea of your accommodation budget? What's your nightly limit ?

Whatever type of accommodation you choose, I'd recommend that someone with 2 young children should consider the location carefully. If you're a long way from BTS or subway, you'll have cranky kids in tow for much of the time - no fun walking around in Bangkok's heat at the best of times but with two tired and cranky kids it will make things very difficult for all of you. Choose something close to a train station.