It's a difficult and unpredictable one. On the one hand you may face having to deal with a double upset, his inability to settle in respite. I've found 2 weeks an odd period. How long would he need to settle in the care home? Is 2 weeks too short that by the time he has settled he is ready to go home, then having to settle into a different routine again? Then again is it too long, resulting in restlessness? Will you be worrying about that during those 2 weeks and will this give you the rest you need?
On the other hand things could go very well and both of you will enjoy a relaxing time and leading to future respite time. Especially for you it could mean a period of recharging.
A lot would depend on how he will be occupied, if this is tailored to his needs and his interests are maintained it could be a very positive experience.
Sorry if this is sounding negative, I don't mean to be but those are the questions I kept asking. I was hoping for a day centre placement, unfortunately by the time I started to look into this the Covid arrived and they shut.
But you know your situation best and perhaps the answer is (and maybe should be) to try it.