Am I being unreasonable?

I’m going to ask this with as little context as possible, because my relationship with my parents is really difficult but I personally believe the answer would be the same if I had a beautiful loving relationship with them.

Scenario:

My husband and I are expecting our second baby in January. We live about 8 hours from my parents and my in-laws live on the opposite coast. My son is currently 13 months and will be (math is hard) 17 months when the baby is born.

My parents volunteered to come down and watch my son while we are having the second baby. They have spent maybe 3-4 visits with him total in his life, so I plan on having TONS of information for them since it’s also an unfamiliar area in the dead of winter.

❗️❗️My question is: am I unreasonable for saying that while they are babysitting my son, neither of them are to drink alcohol?❗️❗️

Even just for date nights with a baby sitter or my sister watching him, we have had a strict no-alcohol policy. When we have visited or they visited us, they can do as they please because either my husband or I are there as well.

The argument will be that my mom will watch the baby and not drink but I am uncomfortable with it regardless.

Bonus question, if you agree with me, how would you handle it with them KNOWING that there will be issues?

For the record, I am not trying to take advantage of their kindness and impose rules while forcing them to be there. If they object, we have friends in the area who have volunteered to watch the baby.