Do I need a re-entry permit if I leave Thailand with a 60-day extension to return later?

I did the same last week we traveled together for a month than came back into Thailand I went to the security together with my wife without any questions I got 60 days again.

But it’s not 100 % guaranteed but I suggest you walk to the security together with your wife

Do you NEED a re-entry permit? That's up to you.

If you leave with a re-entry permit and return, you'll be stamped in until March 5th, which will give you like a week of permission to stay in Thailand.

If you don't get a re-entry permit then you'll receive a 60 day visa exempt stamp if they allow you entry. That decision is up to the immigration officer that you're standing in front of and will depend on your recent history in Thailand. No one here can tell you if you'll be allowed in or not.