I read a similar discussion recently… someone else may have more info on it. If the kids will go to a school then 1 kid can have 1 legal guardian visa for a parent. I guess that means if you put your kids into a private school you both may be entitled to apply for guardian visas.
some airlines don't want to take the risk that someone may get turned away from the border for not having an onward flight within the 30 day visa exempt period (or that of one's visa if short term). This can happen at the airline's expense which is why they can be rather strict about onward flight requirements for someone about to embark on a long distance flight.
For hotels, recommend using Agoda. I have a Thai friend who works support for Agoda working from his laptop at the gym I go to. See him most days as I bring my laptop also for play. So for me if I have an agoda question I can ask support in person. But if you want private condo instead for longer length of stay for cheaper try Airbnb
Some people are over thinking it here but yes the no need for a visa and use visa exempt is most simple. You will fly in and then 5 days later fly out to your next destination. This trip will be your onward ticket requirement sorted - just make sure the 5th day trip out isn’t a land border crossing. And then as others have said when you come back you can get a 30 day extension to make up to your 5 weeks before you fly home. The single entry tourist visa might not work that well as the immigration officer may activate it in your 5 day trip rather than the 5 week one (unless you apply for one later).