My wife and I have valid USA green cards. We are Egyptians. Our daughter is American and lives permanently in the States. We don't like to keep the green cards, as we will never move permanently to the States. We need only to visit our daughter for short periods once a year. Is it possible to submit back the green cards and apply for visit visas? How can I do this?
Yes, this is possible; I have done it, though it was about a decade ago. I can't remember which form I completed to surrender my lawful permanent resident status, but it currently seems to be an I-407. It was surrendered when I was applying to enter the US. Once it was done I was admitted for that trip, but strongly advised to apply for a US B1/B2 visa even though I'm a citizen of a visa-waiver country.
When I did apply, after my return home, the application process was thorough, but it seemed fair, and the visa was approved. However, I don't think the US government plays games like "I'd like to surrender this green card, but only on condition that I get a visa", so you are taking the risk that your visa(s) won't be approved, and you'll find yourselves unable to visit your daughter. Note also that visas can be pretty easily revoked, which is not true for LPR status, and that possession of a visa is no guarantee of admission. You'd be putting yourself at the whims of the current US president and his tendency to make decrees affecting the travel of citizens of arbitrary nations, and you may not wish to do that.
But yes, it is perfectly possible.