K.,
We have a 4yr old girl, and since day one, most of our close friends gave us a nick name of "helmet parents" due that we both are very anal and very protective of our daughter - may it be with family and friends or her school.
Honestly, you are not the only one feeling over protective of your child. You have every reasons to be and never, ever be concern or worried of how the other parents would think of you. Bottom line here is that you are taking precautions for your daughter.
My suggestion would be that you have a one-on-one chat with the parent(s) of your daughter's friend. Get to know them and share with them your concerns and expectation. Until you do so, nobody would be able understand why you're doing things as such. If any of those parents are not understanding enough and in turn would treat things the negative way; then you know that they are simply not the "type" of parents that have similar values or someone that you can trust to protect your child in their hands.
On the same note, you have to have a mommy-and-me talk with your daughter to let her understand the consequences as well as your rational behind your action of being a protective parent(s). Let her pick her top 3 good/close friends that she'll like to invite them to come over to your house instead. That way, she knows that she can still have fun with her close friends and eventually create a bond with someone that you can trust.
Do not feel guilty about it. Just be glad and proud of yourself that you are still getting to know your new environment, and the people around you - it takes time. It's better safe than sorry.
I know it may be easy for me to share all these with you now; my husband and I will have to deal with this too - one day. However, since we've practiced what we preached since the day our daughter is ready for sleepover (at age 2yrs old!) we have open discussion with our daughter and explain things to her. It takes a while for her to understand and comprehend, but she seems to be able to understand our intention. So far, she is just content with the same group of kids(with age varies from 1yr - 11yr) that we all used to hangout together as a group - parents and kids all in one house. She often look forward to meeting these kids.
Something about me:
My husband and I works fulltime, been married almost 8yrs. Our daughter is the only child and she just turn 4yrs old, and is in pre-school. We spend alot of time together as a family as well as one-on-one. I'm asian, and we both have similar "military-household" background.
Good luck to you and welcome to Richmond!
- R. D.