I don' think you have thought this through enough.
If you get a puppy in Feb and then go to work in April you are expecting a 16 week old puppy to be left for two days a week. Much too long a time to leave a puppy or young dog.
The exercise needs will not be the same - the puppy will need much shorter weeks for several months.
You have a baby that has not yet started walking and considering added toilet training a puppy with crawling toddler and potty training a baby at same time as training a puppy and working two days a week.
I would enjoy your baby get back into the swing of being back at work and having a baby and rethink this over next year.
What will happen when you are at work? I ask because a puppy has different needs than an adult dog. Exercise may be the same but he needs training and more socialising. Also my puppy needed to be let out in the garden a lot more often when he was little. It is also worth thinking about whether this is the right time - Puppies and toddlers are not as simple to manage as adult dogs and toddlers. I have a 2 year old, 4 year old and a 7 year old child, as well as a one year old dog. It's been a tough year. x
Am currently on mat leave, will be going back to work for two days a week starting in April. DD is currently 29 weeks. I have a wonderful basset hound. He's very accepting and DD is his baby. However he's fine with DM's dogs being around her and isn't aggressively protective of her. We used to have another dog with him but he's now on his own. He's had to get used to being a solo hound, he's still very nervous about other dogs and strangers as previously he had the other dog for confidence!
So am I insane to contemplate getting a young basset bitch? Was thinking about Feb time as I'll still be around every day for mixing etc. He loves being with DM's dogs and playing with them. In the evenings he plays 'tuggy' by himself, but obviously it's not that great a game by himself!
Housetraining doesn't phase me. Exercise will be the same as him.