I can’t think of how one would replicate a board book with resources typically available at home. Not just the binding, but also the printing would be difficult

I can’t think of how one would replicate a board book with resources typically available at home. Not just the binding, but also the printing would be difficult if not impossible without essentially building your own four color press. I imagine that there are printers out there that can print on thick cardboard, but most people don’t have one of those either. If I were making DIY children’s books meant to be durable I’d probably print folio on Tyvek printer paper and use some suitably durable thread to sew a booklet binding.