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
in case your Tourist Visa arrives in your email after you already entered Thailand visa-exempt and got stamped in for 30 days, you can extend one time for 1900.- THB for 30 more days. Before they are over, just do a border bounce and activate the 60 days stay permit of your Tourist Visa (keep in mind that a TR visa must be used for an entry within 3 months from its date of issue)
if you are in Hua Hin, you can do the border run with a "visarun agency" via Ranong and Myanmar, and back on the same day. This is the only land/sea border to Myanmar that is open for foreigners