What Should I Do?

I will not invite her. Since you are not friends with her yet, it will be awkward for her too. This is what I would do, if you have time before the birthday. Invite her to your house just you and her family and get to know each other. If you both feel compatible, then invite her to the kid's birthday. this needs to be at least couple weeks apart in my opinion.

 

Hi there,
We were in a same situation as you were. We recently moved to a new place and know only two families and I struggled to plan of what to do whom to invite etc. and took lot of stress thinking no friends family around to have your little one feel special having ppl around. But anyways we called those two families and celebrated our sons birthday. Lightly decorated w balloons and ordered a cake and few kids variety’s for food and some for adults. Overall it wasn’t bad. You should go ahead and call those two families and do as what Angela suggested. Doing at home is much better as there are few ppl and easy to host at home.

 

As Angela said u should invite the lady u know to ur home before u plan on calling for the party. But I feel depending on wavelength u Both have and the conversations u share. U would know ur comfort to whether call the new member or not. But personally if I were calling my close family friends. I wouldn’t fight it about that new person just to increase the strength for the party. Go with what ur husband suggests if u cannot make any decision.

 

As others said try to initiate to talk with her and casually you can ask her number. If you feel comfortable then go ahead and invite her. Since you don't no much people around you ...try to invite her and see what she says. If you have her phone number it's easy to text and check with her.

 

Birthdays are about the kids not how many people are in the birthday party. Why don’t you take the kid for a day out to a theme park or the zoo or some place where she will have fun?