I am a director of a childcare center. I think both things could be accomplished - but it needs to be addressed.
1. all older children entering the classroom should take their shoes off. This is older siblings, this is visiting kids from other rooms. Period. The reason teachers and parents wear booties or socks/no shoes is to keep dirt and pebbles and everything else off the floor where babies are crawling, picking up anything they see, etc. Since older kids' shoes are also dirty, have mud on them, wet in rain, etc. , they need to have shoes off too. So our rule was "you can come in, but you have to take off your shoes" (because booties don't fit kids and are too unsafe, they'll trip). That often discouraged parents from this, because it was such a pain to take off their kids' shoes, and that was fine.
2. If they want to visit, they need to be respectful and safe around the babies. So they can WALK in, say hi, perhaps sit on the floor for a minute, but there should be NO running, jumping, etc. Seriously. It's for the safety of the babies, and also you can't have kids sliding, running and swinging without shoes on - they'll fall, which won't hurt them but they'll topple over a baby - even if it doesn't hurt the baby, it will startle the baby and they'll start off the day crying. No fun.
3. Finally, if the reason the older kids are in the infant room in the morning is because there aren't enough staff in the toddler/preschool rooms, this needs to be addressed immediately. Occasionally we had to combine all of our children together in the early morning (first 30 minutes of opening) but the older kids were to sit down and read books.... and this wasn't the rule, it was only if too many people were out sick/late. The plan in general should be that the older rooms are open in the morning, even if it's a combination Twos/Preschool group in one room.
So I'd tell the director your concerns (via phone or in person) and ask whether some of these ideas would work.