Keep your friends close, and your enemies closer, as the saying goes.
I'll try to put a different perspective here. Marami ang nangangailangan ng katulong, maid or yaya, and I believe kokonti lang ang qualified, and/or at the very least, trust worthy na pwede mong ipagkatiwala ang pamilya mo, not to mention ang laman ng bahay mo.
If this girl is a hard worker, she knows her place (na empleyado mo sya at ang mga dapat nyang gawin sa trabaho nya), and she cares for your child, I believe she is worth keeping. She's at the age na highly impressionable pa, you can influence her and help her grow to be the kind of woman that you will respect, like, etc. Kung papalitan mo sya dahil sa paranoia mo ngayon, you'll have to wait and interview so many people pa and in the end, baka mas malalaki na ang sungay nung replacement na mas mahihirapan kang baliin at disiplinahin.
Now, it is up to you how you should discipline this current helper of yours. Think of her as a younger sister. Gently tell her, wag masyadong mag pa cute (don't refer to your husband), be prim and proper sa pakikipag usap sa mga nakakatanda sa kanya, sa kanyang pananamit, etc. Tell your husband na you are trying to create good employee-employer relationship muna kaya he needs to support you by not being overly friendly or close to your helper. She needs to learn your rules and the parameters that you set at home. Kung nakikita nya na si husband hindi consistent sa gusto mong mangyari, syempre, maguguluhan si helper. So you and your husband needs to have a consistent "message" and ways of "handling" si helper. If super nice si husband and goes out of his way to make your helper feel "at home", that is okay, pero not at your expense - and not kung hindi pareho ang pinapakita nyo ni husband. Syempre natural lang naman kay helper to side with the one who is nicer to her.
There's no perfect helper out there. There will always be people who are better than you, and your katulong might have traits that are better than yours. Mahihirapan ka talaga maghanap ng someone who is worse that you in all aspects. And to be honest, would you really want to trust your family on someone who is so much worse than you (intelligence, patience, humility, diligence, etc?). Focus on her redeeming qualities and as for the rest, isipin mo kung ang paranoia mo is more about your own insecurities than her own actions.