The BIG problem, as I see it, is that Mom is in The Wedding Party.
If she were a regular attendee... fine... no children. But in the party itself, when she was ASKED to be, she should have been told, so she could graciously decline to be a bridesmaid (esp. as family is allowed to bring children), or accept on the bride's terms.
To compound the problem, the bride has put the bridesmaid in a TERRIBLE position, by not outright telling her... but just sort of stringing her along with hints.
A wedding invite that does not specifically say "No Children" or "Only children who are in the wedding party" can be taken either way. Although, the bridesmaid would fall into the 2nd category, so purposefully excluding her children when other members of the wedding party can have their children there is outright insulting. But if the invites were not specific about a no-children policy, your sis should expect at least 10-30 children per every 100 adults to be brought along or RSVP'd along with their parents.
One of my brothers is getting married this summer. If it were a "no children" wedding, quite frankly, even though he's my favorite... we would not be attending. Granted, we have to travel, so instead of just having to spend 100-200 on childcare, we'd have to spend several thousand. If it were local, I might be able to see dropping a couple hundred on overnight babysitting... but more likely... I either wouldn't attend, or would attend solo (sans hubby). But it's a very awkward position to be in as a parent and a spouse. When both are invited, but through miscommunication, only one actually gets to attend, unless they're willing to drop a couple hundred to a couple thousand on childcare.
Hints don't work for people who have to spend money and book time. They need to KNOW. And know quite some time in advance.
I'm sorry to say, but rather than the bridesmaid putting your sister in a difficult position... your sister has put her friend in one. Unintentionally, I'm sure.