Prelude

First, it's their fault to take your reservation.  They took your reservation is probably because 1. they didn't have experience about this, or 2. they expect half empty restaurant, so they want more business, or 3. the person who answered the phone didn't know anything, or 4. they didn't want to say No to customers.

We all know 7 + 7 babies is almost the worst reservation possible there is for a restaurant.  No money, more trouble, possible slow down the whole restaurant.  After this incident, they know they shouldn't take such reservation any more in the future.  Your mom asked the server and expected the server to lie "We welcome you and your friends and the babies come back anytime.",  or you want the server to tell the truth?  You said your mom knows the server, so the server might not want to lie.  It might be their fault at the beginning to accept this reservation and not bringing chairs (I don't know a restaurant has 7 high chairs), but I do not see anything wrong at the end though.

Yes, the restaurant staff will feel they are doing you a favour to let you eat there with 7 babies, it's sad, but true.  That's same with any other restaurant unless the staffs doesn't care about money at all.  

Business is business, it's all about money and only about money.  They can't make money off your visit, might as well not do it.  In this case, they might lose money serving you if there is at least 2 groups waiting for a table.