I think the type of party, the age of the birthday child, and the age of my own children would certainly play a role in my assumption.

Having young babies, I would assume that being invited to a 1 year old's party meant that I was being invited with my young family. I wouldn't be taking along my teenage step sons though. Like some of the others, I think I would personally find it a little strange to be invited to a 1 year old's party without my kids. It would be different if I didn't have any of my own. My separation anxiety from my kids would mean that I would decline if it was just me invited.

If the birthday child was older (school age) and the invite was for one of my children that was friends with that child, then I would assume that only that child was invited.

If the party was for a wedding, 21st etc... then I would assume that the invite was for just me (or clarify if hubby was also invited).

If you want to take something good from this situation, then maybe it's that your friend feels that you are closer to her than you realise. If you really would prefer the kids not to come (I know you have said that they can come, but this is in case you'd still prefer them not to), maybe you could just casually say something along the lines of "I'm surprised that your bringing you're hubby and kids and not taking the opportunity to take a break from them and just chill like our other Uni friends". And perhaps then let her know that you're worried they may become bored because they are older and you have nothing planned for older children. Maybe she'll change her mind. I definitely wouldn't be bringing up anything about your feelings towards her hubby and kids.