There's three things you need to apply:-
1. Patience and repetition
2. Patience and repetition
and finally
3. Patience and repetition
The fact that you are on here and asking speaking volumes - it's clear you love her and want to do the best for her (and why wouldn't you as she looks a gorgeous dog). The fact you have 4 kids under 9 years old is also a valid point as you have a busy house, I can only imagine how difficult that will be and indeed you have "quite the pack".
At circa 20 weeks learnt behaviors are already surfacing and, if it was me, I'd be steeling myself for a bit of a journey ahead. Although as she's still very much a pup you'll be able to mould her to fit in with you and your family if you apply the magic three things above!!!
Confession time from me -- we rescued Lab number three six months ago. She's 3 years old and hasn't had the best start in life with most of the puppy basic training clearly missing. The one thing that was a nightmare was her starting to bark in her crate downstairs at 4am every day. We tried everything from leaving music on, lights on, in crate, out of crate and really gave it the best crack with ignoring it.... the patience and repetition mantra.
We have virtually cracked it after six months BUT not perfect like or other two - her Lab wake up call is now about 6am. One bit of assistance we have relented to is a command collar. We use it very sparingly and it only has a beep or citric spray function - never, ever would I use a shock collar.
Please do google Separation Anxiety in dogs and ways to curb it - I hope for your sake and for your beautiful dog's sake you find some methods that help.