I don't think children should be shushed in their own home, or made to feel as if they have to be quiet. They should be able to play in their garden in exactly the same way as they would if DH was at work.
If DS can do all of that and DH isn't getting stroppy about noise - the OP suggests that he's absolutely fine about it - then I don't see why DH can't work from home. The person who is WFH should have to adapt around the people who are living there and don't have the right to insist on certain working conditions being met. But I don't think asking the child not to go into a garden office is an unreasonable request.
Literally the only thing in the way of the DH being able to WFH is a child who won't accept being told "no". Their lifestyle isn't being curtailed, they are free to go around the whole house and garden playing however they want - apart from one room.
What if someone was ill? What if one parent worked nights? The child would have to learn that sometimes the answer is no.
I know MN likes to pile onto men disproportionately - and in fairness, it's often with good reason. I'm not a man, btw, but I don't like the ways things aren't always even handed. If there was a woman on here saying that she preferred to WFH and that her DH refused to stop their child from busting into the room, posters would be queuing up to criticise the man for not being able to parent the child. There's no way posters would be agreeing that the woman had to leave the house.
Why should someone - of either sex - HAVE to go into the office just because it's impossible to teach a 2 yr old that Mummy/Daddy is at work and therefore unavailable? It's a ludicrous concept. There are lots of reasons why WFH might be preferable and in this modern day and age, it's not unreasonable to want to WFH.
Also, with another baby on the way, now seems like the ideal time to teach the toddler that sometimes you can't always get what you want right away. OP is going to need support from her DH after she gives birth, and that might mean explaining to DS that they can't go to Mummy right now.
Honestly, I'm not unsympathetic and I get that it's much easier to shoo DH off to work at the office. But having an extra pair of hands in the house as an emergency back-up could be useful when there's another small baby in the mix. I've suggested methods above that could help ease the learning period - and I've been through this myself with SEN twins so I know it's painful at first. But if both parents stick to the routine, and the aids are used every time, the child will quickly adapt.
When I took my DS to nursery for the first time he cried his eyes out. And he did on the second day, and the third. It took a while but he learnt that he could have fun while I wasn't there, and that I'd always come back for him. It's exactly the same principle.