Traveling with dogs

We are moving to Cambodia and now it´s time to make sure that all things are done.

We have two small dogs and we have decided to fly to from Finland to Bangkok and after that drive by car to the Cambodia. We chose car because there were not any carrier who would have accepted pet travelling in a cabin (as they will do from Finland to Bangkok).
We are prepared our dogs papers and vaccinations, and all should be done, but I´m still worried is all in order.

In Thailand there should be 1) a health certificate in English by a full-time authorized veterinary official of the government (checked - ok), the animals must come from an area where animal diseases are under control (checked - ok), the country has been free from Rabies for at least the past 12 (twelve) months (checked - ok), the dog is vaccinated against Leptospirosis at least 21(twenty-one) days preceding departure (this vaccination is taken in 2 parts, 1th is valid 1 month and after that 2nd part should be given, and then vaccination is valid 1 year. our dogs have got only this 1th part and it´s valid over we´ll arrival, we were planning to have this 2nd part in Cambodia. DO ANYBODY know is this enough ok or do we need to wait until this 2 part is given??) and the animals shall be vaccinated against other significant infectious or contagious diseases i.e. Distemper (checked - ok).

I think I we have all what Thailand demand, we are allowed to arrive to the Cambodia.
One think I´m worried as well, is it ok to arrive with a dogs by car or should dogs arrive always only by an air plain?

If somebody have a good advices and/or a first-hand experience I would highly appreciated yours help!