The most concrete approach is to ask your employer in writing whether there's actually a contractual clause that guarantees you full remote work, or if the change falls within their prerogatives. It's less straightforward than it sounds: if your individual contract says "work in agile mode" and not "work in agile mode until further notice," you've got more solid ground to push back on. If instead the contract is vague and just says "work mode to be agreed upon," then technically the company has a lot of wiggle room.
That said, if you have real needs tied to young kids (school at home, no grandparents around, that sort of thing), you can try negotiating: a lot of companies are more flexible than you'd think if you present it the right way. I know people in my circles who managed to get 2 days in the office instead of 3, or split schedules, just by documenting their needs. It's not a guarantee, but it's worth trying before you accept everything as is.
Last thing: check if your industry's collective bargaining agreement has anything about parents' rights (leave, family support). Sometimes people only find out later that they had rights they didn't know about. If the company keeps pushing and you really do have an airtight contract, then yeah, it's worth getting a quick legal consultation, maybe through a union if you're a member.