PUPPY-PROOF. EVERYTHING.

It doesn’t matter if you think, “Oh, there couldn’t possibly be a way for an eevee puppy to get in there.” No. No, anonymous. You absolutely must puppy-proof everything. Put locks on the cabinets where you store your household chemicals (and be sure that it’s a cabinet well above floor level). Invest in gates. Invest in gates for the gates. Cover your wall sockets. Secure your valuables and fragile items. Consider bolting your furniture to the floor while you’re at it. Place your wires well out of reach and cover them with repel. And if you happen to have any important papers that you don’t want to see ripped to shreds, lock them away. Eevee puppies are extremely curious and tenacious. They will cause mischief if they can find a way to do so.

Other than that, simply ensure that the mother has a safe, secure place to lay her egg(s), as well as plenty of food and water, and perhaps watch videos on how to assist in delivering and caring for eggs. (Or perhaps don’t do the latter, as the mother may become territorial while her egg is incubating, and in any case, most mother pokémon will know how best to care for their young. Umbreon especially are prone to biting if you get too close to either her eggs or newborn pups.)

Best of luck!