I know it can be hit or miss, but you might find a used but solid PS4 on Craigslist that may be a little cheaper too. I just did a search on my local Craigslist and someone in my area is selling a new one for $225. Used ones are about $195 in decent condition.
I totally forgot about the PS+ thing. The one nice aspect about couch co-op is anyone can play D3 on the same console as long as the primary person has a PS+ account if I remember correctly. So it would indeed require a separate PS+ account on another PS4 in order for you both to play together.
I did a quick search for discounted PS+ subs and CDkeys has it on sale for $35 at the moment on eBay. I'm pretty sure I've taken advantage of this before in the past.
As far as a copy of D3, get a used copy of Reaper of Souls maybe on eBay for $12-15 and get the necromancer pack for $15. PSN had a sale at the beginning of April for D3 Eternal Collection for $20 so you can always keep your eye out for that, though I prefer discs to digital.
Looks like my original post got lost when replying. haha
In any case, as a dad of two kids and a married husband of 13 years to a non-gamer wife, go for it.
As long as you're taking care of your family and have your priorities in order (based on above it seems like you do) and most importantly your wife is in agreement, then you are in a good spot.
It's easy for parents and spouses to talk themselves out of things they want and like but again, if you're taking care of the things that matter, well, life is just too short not to enjoy simple pleasures while bonding with your wife, family and friends.