It is for health & safety - buggies can hinder safe exit in case of fire.
If you really can't manage to carry your mindees in, then I'd write to the nursery manager. I've found that telling schools/preschools isn't always enough - your opinions can easily be dismissed and forgotten. Twice I've put my concerns in writing to our school and, what was overlooked for weeks, was suddenly resolved in an afternoon.
Would explain that you take your responsibility as a Registered Childminder very seriously and you have to keep minded children within sight and sound at all times to meet the requirements of Ofsted and your insurance provider. As its not physically possible for you to carry 2 mindees and dd2s belongings you are seeking a compromise to resolve the situation. You have already offered to pop your head round the door, (is there anywhere inside you can stand and still have sight of your buggy outside?) but if thats not acceptable to the nursery, you would have no objections if they would prefer to bring dd and her belongings outside to you.
Childminders must not leave minded children unattended and can only leave mindees in the care of others in a real emergency situation. If you check with your public liability insurance provider, I think you'll find you're not covered while children are not actually with you. If you ask them to confirm in writing, you can enclose a copy with your letter to nursery.
Similarly, I expect Ofsted would take a dim view of the nursery's suggestion, can't imagine an outstanding grade going to a cm who leaves mindees unattended, can you? Although I've not spotted if it says in EYFS specifically that you can't do this, it goes against the view of every Inspector I've met.
Parents can legally choose to leave their children unattended if they want to. Childminders can't. We have a few more rules to follow than parents do. And rightly so - its a huge responsibility taking care of other people's children. Its not unreasonable for parents to expect the person they are paying to care for their child to keep their child close by the whole time.
Its unlikely that mindees would come to harm outside the nursery. But we cannot take chances with other people's children, however small that chance may be. If the child isn't within sight or sound they're not technically in your care at all. You can't possibly keep a child safe from harm if you can't see OR hear them. JMHO