You’ve started with “Let’s say…” Is this a real situation?
If the child’s father is still alive, I don’t see how you’d be able to adopt, unless he doesn’t have custody. In that case, the adoption would be his, and you’d likely be appointed some form of guardianship. Or are you planning to adopt both of them?
Despite a platonic relationship, you’d still be giving everyone the wrong impression if living together. You’d need an actual title, like nanny, housekeeper, or governess/tutor, and receive some form of recompense for it not to be cohabitation.
Your mention of when everyone is out of the house, could you be a nun, is probably along the lines of lay contemplative. Certainly that is permissible, and encouraged, actually. Keeping the house quiet for the sake of recollection, following a prayer schedule, etc., is plausable. St. Francis de Sales says that due to the father being out making money to support the family, the mother is the one who should be the most pious for the sake of setting a good example for the children.
The cloistered life is fecund with souls. Right now, that’s a motherhood that is almost more desperately needed than blood/physical/adoption motherhood. It takes the prayer and penance of the cloistered religious to bring down the graces of opening to adoption and proper parenting on those in the world.
If you’re already working with a cloistered monastery, then, by all means, persevere. You will be looking at them, as they will be looking at you, with a view to discerning whether you are really called there. The second link under my signature is my particular ministry within our new congregation (first link). I have been praying for and promoting the cloistered life for over 30 years now. Find a Visitation monastery, and see if you can go on silent retreat there, and see what the cloistered life is like.
Blessings,
Cloisters
http://cloisters.tripod.com/charity/
http://cloisters.tripod.com/