Most tulips aren't reliably perennial and only last a year or two. I plant more every year and if they do come back, I see it as a bonus. Sorry!

Will they survive and come back next spring if we transplant them now? Is there anything special to do before/during/after moving them?
It would be best if you were to leave them until the foliage has dies back a good bit, maybe about 6 weeks after the bloom has faded.

Then dig your bulbs and allow them to air dry (in the shade somewhere) before storing (cool and dry) for planting this fall. Fall bulbs moved in the spring run the risk of rotting due to warm soil temps and moisture. Bulbs dug before the foliage has faded will likely not bloom next year, as it is the fading foliage that feeds the bulb for next years bloom.

Also, as lady said above, most are not very perennial. It has been discussed here that maybe they would be more likely to bloom the next year if they were lifted after the foliage dies back, and then replanted in the fall after soil temps have cooled.

Sue