I would feel really odd going to a child's party without my children (if I had children), or my husband (if I had a husband) to be honest and would find such an invite quite strange.

And, even if I were only friends with someone and an invite had only my name on it, I would assume that my husband and children were invited too as that's just what normally happens.

To answer the opening question, I don't actually know how you would word it to say they aren't invited and not sound rude.

Eta - If you verbally told these ladies it was only for them and not their children/partners (as someone else suggested), what would be the reaction when they saw other people there with children and hubbies? Would make me wonder why you didn't want mine there iykwim and could make your friendships messy.