Wow. The sexism on this thread is incredible.
Fine for baby to be taken out of the country, away from his father, by his mother.
But to be left in the country, with his father, whilst his mother is away is horrifying. It shows the mother is unloving, uncaring and will lead to psychological damage for the baby.
If it's fine for the baby to be away from one primary caregiver for 10 days it's fine for him to be away from the other. Doesn't matter whether it is his mother or father if you share the parenting equally and both have a living bond with him.
I honestly think it's fine to leave him with his father and nanny in familiar surroundings and his familiar routine. Yes, you will miss each other but it is only 10 days. I'm sure it will be far harder on you than it is on him.
Really, it makes sense to leave him. We recently did a 16 hour long-haul flight with DS, aged 10mo, and it was horrible for him (and us!). And he was definitely jet lagged on return. I wouldn't put him through it again unless necessary whilst still so young.
It will be nice for you and DD to have one-to-one time and similarly for DS and DH to have one-to-one time.