It's a bit early for you to know how you'll be feeling then.The baby doesn't seem that real to you now but when he/she is 3 months old I'm not so sure you'll want to go...
I don't know,if your parents and the dad want to and are capable of taking care of it...You're mom had 4 kids,I'm thinking she's very good with babies,she shouldn't have any problems.And you might regret not going,it's a great experience.I'm going to Spain in August(I'll be in third trimester,they don't recommend long flights then,but I don't want to miss it

)...
Plus,one week is not long.
Do your parents know that they'll be looking after a baby?