Putting the financial part aside, do you and your husband want a lake house? Is this a way to get the vacation home you always wanted, while letting it pay for itself?
If so, I'd do more research, but then go for the lake house! Have a chat with your CPA, but there are some very nice benefits with, say, going to work on your property on Friday and Monday, but then enjoying the weekend at your lake house and being able to deduct travel and some of your meals.
Airdna.com is a good resource for estimating vacancy and revenue potential. Property management on STRs is expensive, but it doesn't have to be all or nothing. I self manage our STRs and communicate with guests, but I have a cleaning staff, backup cleaning staff, and a handyman who can typically respond the next day. With remote rentals, you just need better contingency plans. Is there a nice neighbor who could, worse case scenario, run an extra blanket over or see why the breaker isn't flipping back on. With our local STR's I get maybe 1-2 calls per month from guests needing something outside of my normal cleaning/maintenance process; and it's usually simple requests for things like an extra blanket or the cleaning lady forgot to restock toilet paper. The nice thing about Airbnb is that people are pretty forgiving. As you bumble through getting your processes figured out, there's not much that a partial/full refund won't remedy.
Is it remote? Will you get year around traffic, or is it a seasonal destination? As you start crunching numbers, think through your plan for a worst case scenario. On the one hand, at $325/night, you only need 8-9 nights per month to cover your mortgage, utilities, and cleaning. However, what if you only got 5 nights/month for 3 months in row—would that put a huge burden your monthly finances? If needed, is there enough demand that you could slashes prices to $75/night+cleaning and keep it close to full?