Everyone has their own way of finding a 'path'.
I had a double major in Education & Psychology with a minor in Computer Science.
As a result I can be sensitive to my client's needs and 'teach' them how to do things the 'right' way. Plus, I do quite a few high tech visas .. .because I can 'speak tech'.
I may be in the minority but I do NOT think that speaking a foreign language is a prerequisite. Although it doesn't hurt ... it sort-of limits you to a particular population.
No, you will not get free medical insurance if you get greencards.
Your kids need to sign I-864 affidavits of support ... guaranteeing that THEY WILL PAY for your needs for the first 10 years that you are in the US, or until you become US Citizens, which takes about 5 years.
Sorry the answer is no ... the spouse of a greencard holder can not stay in the US while they are sitting on the 2+ year waiting list.
I suggest he go back to school for the next few years ... or find a cap-exempt H employer.
I do not think that this is the 'final' word in this area. Things are warming up for the US Supreme Court to step in.
For people who don't know what you are talking about, here is a link to the case:
Since your OPT expired ... stop working ... immediately.
Talk to the lawyer that did the H papers to see if there is an RFE or appeal possible.
You currently have no status and ... depending on how the denial is written, you may be accruing unlawful status.
Meet with the company's immigration lawyer ... not someone in HR .. not an immigration 'team' ... a real live lawyer.
File an I-824 and grumble at the outrages fee they will charge you ... but, you have no choice.
As for your dad calling ... yes, if HE calls, they might give the receipt number ... but that's not 'enough'.