We are using Webgility but we are not live. Webgility pulls sales from our online store and puts them into QB we also process our online sales through Webgility which sends the status to our online store which notifies the customer. Again we aren't live yet and we have had some issues with Webgility so i am not recommending them at this time. Webgility or a similar software can pull sales from multiple channels, like selling on Amazon or with Home depot, it also connects to UPS for shipping.

Our issue is basically inventory managing and keeping it in sync. But if the Square POS system doesnt update QB inventory and only transfers sales which QB would adjust its inventory at that point, then i think we are good, other than getting our online sales to delete from stock in the square inventory. I will reach out to Square as i know they can sync to my online store but i hear bad things about that.

 QB would update inventory based on sales from the square POS and my online store. Also adding stock based on my PO/Bills. I think this is solved for us if i can get the online sales to delete stock from the POS system and not send those sales to QB.  And please correct me if you see any issues with this.

I am new to all of these software's and have been navigating this for over a year. We  are still trying to find the best combination that all works together and is as automated as possible.