How much would you pay??

So right now I have a 2 1/2 yr old and a 6 month old babe. My partner and I are planning to go on a vacation next winter when they will be 3 1/2 and 1 1/2 we want to go for one week to Jamaica and I'm really excited because I've never left the country before or ever traveled. Don't judge me but I really don't want to bring our sons..it would be super expensive to have to pay for their tickets as well and I just want to relax! Don't get me wrong I would miss them like crazy but I know they would be perfectly safe and supper happy staying with my cousin (she's my best friend) her son is 2 years older than my oldest. I haven't asked her yet obviously because it's so far away lol but how much do you think is acceptable to pay her? I mean it's a whole week with her own kid she's gotta get ready for school everyday then my 2 small kiddos as well I'll want to cover the cost of food for them and also the hassle of having them all day and all night for a whole week! I was thinking 500$ but my partner thinks that is a bit too much...I kinda feel the opposite. By no means are we rich but it's alot to ask for sure. How much would you pay? Or want to be paid if it was you in her shoes?