Can one get emergency mainland visa in Phu Quoc?

Hello huajules, and welcome to expat.com.

Sorry to hear of your predicament. I'll try to help you with this and offer you some options, but first I've a couple of questions.

   Unfortunately 3 out of 4 members in my family did not receive our evisa approval in time before we flew to Phu Quoc.

What are the "Permitted To Remain Until" dates showing in your and your children's passports (full 30 days permitted?)? What "Permitted To Remain Until" date is showing in your husband's passport (full 90 day eVisa?)?

Due to TET, immigration office will be closed for a full week  We are supposed to fly to HCMC this Thursday (in 3 days!)...

What time on Thursday (the 15th) are your flights?

...and learned that even if our evisas come in that day, it won't be valid since we are already in phu quoc.

Correct and though you are already aware of this, for the benefit of casual readers of this forum, eVisas are activated/made valid only upon entry to Vietnam through an international crossing (air, land, or sea).

Does anyone know if i can go to phu quoc immigration office on thursday (first day it reopens after TET) and try to get a mainland visa approved in a few hours?

It's certainly worth a try. Travel visas, allowing foreigners to leave Phu Quoc and travel to the mainland, are available but your time constraint has me concerned.

I know we can try to do a visa run but it seems to be quite complicated or potentially very expensive if we book 3 flights of out of phu quoc, into another country, and then fly into HCMC from there.  doesnt seem to be quite worth it for a place we were only going to go for 2 days anyway.  Plus my husband only has single entry visa and cant leave vietnam with me and the kids. What to do?       -@huajules

It might be in your best interest to immediately enlist the aid of a travel agent. Let me know whether you'd like to try this option, and I'll put you in contact with a trusted, long-time member of expat.com who has been using the services of his agent for many years. That said, immigration might just come through for you on Thursday and save the day.

Okay, looking forward to hearing back from you. It would be great to hear how you eventually decide to navigate this issue. We'd certainly appreciate it and your experience/report will help future travellers who find themselves in a similar situation.

Once more, welcome aboard expat.com