In this case I'd recommend getting one single-entry tourist visa in the U.S. prior to your departure and then a second, single-entry tourist visa in southeast Asia.

The Vietnam embassy in Bangkok has limited hours, maybe an hour or two in the morning and an hour or two in the afternoon. Getting a visa there requires two trips; it's best to drop off your paperwork/fee in the morning, then go back the next morning. Same day service is available but it does take all day and costs quite a bit more. All applications get faxed back to Vietnam for approval.

Embassies and General Consulates of Vietnam in Asia - Oceania

EMBASSY OF VIETNAM IN CAMBODIA
Add: 436 Monivong, Phnom Penh
Tel: (855-23) 726 273 / 726 274
Fax: (855-23) 362 314
Email: [email protected]
Consular: Tel: (855-23) 362 531; Fax: (855-23) 427 385

EMBASSY OF VIETNAM IN THAILAND
Add: 83/1 Wireless Road, Lumpini, Pathurnwan,
Bangkok 10330
Tel: (66-2) 267 9602
Fax: (66-2) 254 4630
Email: [email protected]
Consular: Tel: (66-2) 251 5837; 251 3551;
Fax: (66-2) 251 7201

http://www.vietnamembassy.or.th/visa.html

http://www.vietnamembassy.or.th/major.php?pointer=100