this is not possible. Immigration at the airport will see on the central computer that she has been issued a tourist visa, and they will insist she gets stamped in on it. She cannot just ask for a visa-exempt entry when she already holds a valid visa
he might need a financial proof for the application to the 90 days Non-Imm-O visa, not only for the application to the extension. I can't open the website of the Thai Embassy in The Hague to check, though
applying for a 60-days Tourist Visa at the Thai Embassy in Vientiane, is the best option. You need an appointment, though, and the processing period can be up to 3-4 working days. NOTE: In Vietnam or Malaysia the requirements for an application to a 60-days Tourist Visa are much stricter and more complicated than in Vientiane