In a tough situation, need some advice

I got a job offer that I need to take. They need people immediately and I’ve been trying to compromise with them but they’re barely budging. NF’s are going on a 2 week vacation starting this Saturday. The place wants me to start the first week of September. That would leave NF a week instead of ‘2 weeks’.

I’m notifying them today that I’m giving my notice but I feel terrible that I can’t stay for a full 2 weeks when they get back. The kiddo is also special needs so it’s a bit different than regular nannying.

Asking for advice and some insight on this.

Update: Told them, went well!