Irrespective of the rules of the dowry game; a foreigner is entitled to his own "culture and traditions" to play a part of the "deal"
After all, it is HIS money
Let's get something straight: Dowries are NOT obligatory, if they are agreed to, the idea is for it to be a show of good faith in terms of the ability for the new husband to be financially sound - basically, it is a formality. In Thai rak Thai cases, sometimes the parents of the girl will deny marriage to those men unable to show willing but in many cases also, if the man is known and respected the dowry won't be pushed.
I have been to a few weddings of both persuasions, Thai/Thai, Foreigner/Thai, where dowry has been a feature. I have seen all the money on the ground in front of the couple where beforehand they went to the bank and had it all changed into B20 notes to look like a lot of money - this is accepted with good humour.
In many cases the money is given back to the couple as it is anticipated that while it might all have originated with the husband, it will later be shared as part of the spirit of genuine compatibility between them.
Dowries should not be considered at all if the bride has been married before and/or is not a virgin, so this obviously excludes any children. This does not stop those parents (often in league with their daughter) to extract what they can from a gullible or uninformed foreigner. "Love" might be tested to its extreme in these situations