Your options are not mutually exclusive. I highly recommend crate training for a long list of reasons though, but that does not mean you cannot also make use of a pen, when you are around but cannot "manage" or directly supervise because of the baby.
my friend uses a crate within a play pen when the puppies are younger and hat's a good set-up. She is crate training the puppy but when she cannot get home for a few hours sets-up the puppy in the pen with a potty area.
The pen may keep the puppy contained when they are younger but a 7-10mt ld lab is getting big and the pen may not contain them - and they may still be destructive. So I would start crate training right away in case you get to that point, so you are not STARTING to crate train at 10 months (it's doable for sure but easier to start sooner).
A baby a toddler and a puppy is going to be a crazy amount of work. Make sure you have plenty of time to exercise the puppy and most importantly TRAIN. Especially as they hit the teenage stage, they need an hour of free play exercise a day, start planning ahead for that (dog walker, doggy dacyare, someone playing with the dog while the other is taking care of the kids, etc.)
the one thing about the pen is you need to be on top of the dog's potty needs. Part of the bonus of the crate during potty training is they won't want to soil where they sleep to is buys you time. But with a play pen they have more room so are more likely to just pee. So make sure that play pen time is after a good potty break. OR just have some sort of litter/potty area designated.