So you have kale and greens (lettuce? mustard? etc) in "tubs" - how big/how deep? Are they out in the sun or indoors - under lights or in front of a window? Are they going into the next size up container, or the final resting place into garden soil? And where are you gardening (zone)?
Kale and greens are pretty frost hardy as long as they've been hardened a bit in the sun and outdoor conditions. They can actually be thinned and transplanted at any time, planted deeper than the level that they are separated at, which will help with the flimsiness. I actually transplanted my greens and kale etc from crowded cells into individual cells at less than 2 inches tall. The key is allowing them to settle down for a few days to adjust after transplanting - I use the floor of my garage to keep them out of the sun - and you also need to be sure they are well watered as they are forming new roots. Poor drainage and heavy soil will make it tough for them - I transplant into soilless mix (and even use soilless mix in all of my garden containers) because it is sterile, absorbent and has really good drainage.
good luck!
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