Though it is nonsense to some, do yourself a favor, sacrifice now (both sticking with the cars you have at least until you have to turn in the lease, and lifestyle-wise), and save and buy for cash.
Personally Ive never found that used cars are a really good value. Ive bought used cars, but they always need some work to make them 110% right to my liking. Sometimes ive had no choice, like my old diesels, so it is what it is. But for a late model car, Ive never found that the amortized per mile cost benefit of some slight depreciation (look at real selling prices, not some claims that they all loose 60% when leaving the lot) pays off in a big way. After all, a used car or new car will both need work at, say, 100k. If you buy a car with $45k for 50% of the cost of new, the practical per mile cost when repairs are needed at 100k is going to be roughly the same.
No loans is best. Save for what you can afford, buy that. Dump the lease at its termination unless there is a real good deal or another sensible reason not to, and get away from it - dont re-lease to getyou into more car. Im OK with a low interest car loan if you have a good plan to pay it off quick, like
Your biggest issue is that youll need a replacement for the Mazda, and arent going to escape that. Could you pay it off
I can see the need for a bigger car, given that you may have two rear-facing car seats - new guidance says that 2 years is the recommended date before they should go forward. I can appreciate the effects space-wise to fit two rear facing seats.
But to span the gap, it does not look like it is readily in the budget, so I might try to find an old reliable caprice wagon that was owned by a grandma to cover the time being until things get set right - that is one possible backup plan that you could get into cheaply... But be smart about it, buy quality and make sure you see receipts. Dont borrow from a 401k, not smart.
Good luck and let us know if you have any other questions... I know you can figure out a good path on this.