OP, I think you've done absolutely the right thing in asking for help and advice. My advice is don't do it, but you've explained that your DH is adamant. I don't think you should be getting a hard time over something that doesn't seem to be in your control. You're asking for advice on what to do, which shows you care.
Firstly, the puppy needs it's own space and it definitely does not need puppy pads. We used to put one down on a night to help contain the mess but what actually worked was using a command word. You say the word when they start to pee or poo and eventually they associate the word with the action. You should be putting the puppy outside every hour or so, and every time it looks like it's going to go. They do catch on pretty quickly.
You need to remember that they don't like to toilet where they sleep or eat, so penning it in with a puppy pad is distressing. Keep on with the lifting outside until it gets the message, they it will want to go outside and start to ask. You need to do this over night too.
Once you've cracked that you need to work on basic commands, mainly recall which is the one which will keep it safe. Use it's name often, make coming to you the most exciting thing ever - whatever else it's distracted by can't be as exciting as you so it will always come back to you when you call.
Don't feed it human food; don't feed it left overs and make sure you get a list of foods which are poisonous to dogs espresso since you have children. Check what food it's been on and continue to use that, if you change then it has to be gradual.
Labradors are notoriously energetic, it needs to burn that energy otherwise it will become destructive and aggressive.
I don't think your nanny should be left the responsibility of the puppy, unless she is a dog trainer of course. I think in this situation you need to have a professional work with the family and the nanny at the start.
I can't help thinking this dog is going to end up being badly behaved, untrained and a hindrance on the family which is an awful fate for a puppy. You sound like a lovely person OP, you are concerned about the welfare of the dog. Your DH sounds awful, if he's given you an ultimatum I'd take him up on it.