What are the visa options for expats in Thailand if my wife is obtaining her Thai passport?

Mother is thai, get their Thai citizenship for the kids. For you, marriage visa.

Your wife could get an ancestry visa whilst waiting to sort out her passport. I have no idea what that could mean for you though.

Thailand ancestry visas | Thai Citizenship

The most practical and efficient Pathway is:

For your Thai Wife to successfully Reclaim her Thai Citizenship (Thai Citizen at Birth) and get at least her Thai ID Card issued by a local Thai District Office (Provinces: ที่ว่าการอำเภอ / Bangkok: สำนักงานเขต ), and then, subsequently, your Thai Children (Thai Citizens at Birth also) to also successfully 'Reclaim' their Thai Citizenship by getting their Thai Birth Certificates ( สูติบัตร ) issued by the Thai Embassy/Thai Consulate with consular Jurisdiction over their place of birth outside Thailand

From at least your Thai Wife successfully Reclaiming her Thai Citizenship, then there are Thai Visa and Extension of Stay options for your family (as immediate family of a Thai Citizen)

Passport usually 3 days can be done in one day if collect

If she gets her Thai citizenship recognized, best thing to do for her would be to leave and return using the passport, that way she's in Thailand as a Thai.

For the kids, you would want to get them Thai citizenship as well so they don't have to worry about visas either.

Without her having Thai citizenship, then you all have to worry about visas. You must have at least 21 days remaining on your current permission to stay in order to apply for an ED visa conversion inside the country, and that's only after the ministry of education has given your school approval, which can take up to a month. Also the only ED visas that can allow for dependents are those for attending a university degree program. Language school or Muay Thai and other informal education does not allow any dependent visas.

For the children, them going on overstay isn't a huge deal, as there is no fine for children under 15 and anyone under 18 cannot be banned.

Once she has her citizenship, then get the children citizenship, and then you can get a non-O visa based on marriage to a Thai.

Register the kids birth with the local thai embassy for where they were born and they won't need a visa (a little more complicated than ive put it). As for you non-o marriage.

Your wife having an ED visa won't cause her any problems in the future as she is a Thai Citizen, you on the other hand will likely have issues as its a widely abused visa so I would avoid it at all costs if you can.

The kids don't need a visa as their is no fine nor punishment for children overstaying so while you register them as thai citizens you won't have to worry about their visa status, but if you are strictly wanting to get them a visa then, yes they can be put down as dependants on a ED visa (not sure about short-term ED visas though (as in non-university courses such as language)