induce?! What do you think?

Ga
I'm going to ask my doctor to induce me on the 23rd of June. I'll be 38 weeks. But I'm hoping she will do a membrane sweep two days before at my appointment. I would have no problem waiting until full term but I have two other kids and the only time my dad can take off is the week of the 26th and my mom is coming into town from Maine on the 23rd. I don't trust anyone else with my kids and my two year old doesn't do well with anyone besides my dad. This will be the the first time I've ever left him. I'm already so nervous and I don't know what I'll do if my doctor says no to the induce date. Do you ladies think I'll be denied?