As the mother of a son who has a congenital heart condition I have sympathies all round to be honest. DS didn't have to shield when Covid struck as he isn't on medication ('just' had a few heart procedures since birth to manage his condition).
When the kids went back to school after lockdown, DS did too. My manager (I work in DS's school) arranged for me to work solely with DS's year group so we could keep his (very large) bubble intact.
Now everyone's back to 'normal' we're still careful. We do go out but we go to places that we can book or we happily walk out if it gets too crowded. We'll go to the cinema but we book aisle seats on the cross aisle walk way so we're not surrounded by people if it's busy. Same for the theatre - we try to get seats near the front or very back and on the aisle. We don't go to restaurants now that are 'turn up and squeeze in' and we won't be going abroad for a while. DH has been lucky as his company is offering various WFH options and he's taken advantage of that. Most of his department have and it's working well. As DH has to travel from one end of the country to the other if he goes into the office (his office is literally 500 miles away - redundancy meant no choice for where the next job was) he's asked and got one week in the office, three weeks wfh. He WFH for seven years when DS was born so he's very used to remote working so there's no problem with work ethics.
Although DS is back at school and we're back at work, we still try to mitigate the chances of getting Covid as much as we can. It's possible to go out and still be vulnerable. Sometimes things have to be done but some things that keep you sane or are enjoyable, have to be looked at for risk if you have a vulnerable person in the family.
Ultimately OP, you have a point to take to management that you're all sinking under the weight of being one person down physically. You don't have a say in whether this person should return and saying the family go out or the kids go to school makes no difference - it's the risk/benefit of those things that matter to a vulnerable person. Going out for the day helps with mental health but may take a degree of planning to keep safe. The kids have to go to school. A partner WFH takes away some of the extra, unnecessary, risk.
But you have a right to have all hands on deck so management either have to find the person different work, employ someone to help you or work something else out. No one has a 'right' to work from home but some people need it in order to carry on, are worth it to the company and your management obviously feel this person falls into that category.
Don't bring up 'his wife does this or his kids does that' as that just comes across as nosey and bitter. If his absence is causing problems for the team, that's what needs to be addressed. Stick to that.