as long as you don't work or study in Thailand, or are on a DTV, you cannot get a visa based on your family "dependent" of you. You can get a "sponsor" visa as the parent of a child that is attending school in Thailand.
rather the emphasis on "some embassies". . . mainly those in the passport holders country will not allow an application if he has no residency. In countries outside of Thailand the applicant just needs a proof that he has entered the country and is currently staying there
you can buy the "Family ELITE Privilege Visa" however your daugther at age 18 is too old to still count as a member of the family, and will need her own ELITE Privilege Visa. With this visa, you can leave and return, no hassles, no Immigration checks only have to extend every year for the next year for a fee of 1900 THB
so far so well , , , , , but the real fact is, he won't get stamped back in for another year unless he shows a new health insurance F.I.C. valid for another year. His multi re-entry permit is only good until the expiry of the validity of the visa, and it only allows him to return and getting stamped back in for the duration of the initially stamped (first year) stay permit
IMPORTANT !! . . . what you need to show upon re-entering Thailand after a stay abroad, if you are still within the one-year visa validity, is a NEW one-year health insurance. Because otherwise you will only be stamped in for the rest of the stay permit you recieved when you first entered Thailand on your O/A visa. You need a new 1-year insurance and have to present this insurance form and the F.I.C. to the border official, if you want to get stamped in for another 1-year stay permit.