Birthday party invitation

amaite

This is for a birthday party...so, usually on an invitation if I want the person or couple to come with their kids, I put 'and family'. One of our invitees is known for showing up with multiple extended family members, even if she is the only one invited. I was going to individually name everyone in the household on her invitation, because writing 'and family' could result in her showing up with siblings, aunts, uncles, cousins, etc. and their significant others, but I'm worried it could happen anyway even if we name the individuals we are inviting, and we are hoping to keep the party small. Wwyd? Go ahead with naming individuals? Have an awkward conversation with her beforehand? Wait and see what happens? As far as rsvping, her track record isn't so great. The last time we invited her to something, she rsvped for herself, and then showed up with 4 extra people. We commented that we thought just she was coming, but she didn't seem like she thought it was a problem, and we didnt want to be rude. And when she rsvped to someone else I know, she rsvped for 3 people and showed up with 11. We do really want her and her 2 kids to come, just without extra people who we dont know or don't know well.