You do not need to use the other passport. It is possible to enter Thailand on a 30 day exemption and then extend for 30 days at the immigration office. Then, before your extension runs out, fly or use a land border crossing to Malaysia. You should spend a few days in Malaysia and not immediately return the same day. Or, go with a visa service. Then, cross back and enter on an exemption and extend for 30 more days. Immigration seems to allow 2 land crossings per calendar year and 'unlimited' air crossings. Have you 'return' ticket and Thai address ready. Many people have had success with this method, but at any time an Immigration officer could deny; however, unlikely. Good luck.