Wait, it is unprofessional to have a pet? I work with so many professionals and have never come across that before! It's a normal thing! No, employers can't reasonably expect a professional standard office in your home, that is mad.
Of course it isn't unprofessional to HAVE a pet - but it is unprofessional to let it walk all over your keyboard during an online meeting, or interrupt the meeting expecting everyone to coo over it. I had this happen while interviewing someone! (their cat, not mine...).
Staff meetings where we all have stuff to get through but spend ages saying 'hello' to little Dominic...and then Evie from another household wants a turn, so why not let Fraser show off his Tae Kwando moves...
Now that offices are open again, and where WFH and home educating are a choice, why on earth should an employer expect anything less than a full professional presentation? And some people work with highly confidential material or material that needs to be kept secure or very sensitive conversations. Or dealing with clients or other consultants whose time is a lot of money.
WFH is in general a privilege or perk - there is the tax break for using your space, time and money saved on commuting.
Most people do manage their workload professionally and productively. But the OP needs to be sure that she and her DH can continue this with young children at home.
It all depends on the nature of the job, and the nature of the kids, I guess.