Thank you for your question!
One of the main differences between Seremos muy cuidadosos con ambos and Ambos estaremos cuidando de ustedes is that the second one is a continuous verb tense - as seen by cuidando "caring / taking care" - and estar must be used with continuous tenses.
The trickier part is why ser is used with cuidadoso. Some adjectives tend to be used most often with ser or most often with estar; cuidadoso is one of the ones that tends to be used with ser. You will only very rarely hear it used with estar. As for why this is, I would say that you are on the right track with your impression and ser is used most often with cuidadoso because it implies that permanent state or defining characteristic. It would sound strange if, when reassuring someone that you will be careful, you implied that this carefulness would only be temporary.
I hope that this is helpful! Do let me know if you have any more questions!