this is quite a complicated issue.
i think that the best thing u can do is just be there as her 'aunt'... give her all the love u must give her, she will need it.. don't push her away...
BUT make sure that it is a 'auntie' kinda love, u knwo what i mean?
of course u can hug her, of course u can give her kisses in the cheek...
but if she ever tries to kiss u like a lover would, make sure u put a stop to her..
try NOT to spend more time with her than u spend with the son...
so that she knows that you DO lover her, but that you lover her as tho as she were your 'daughter' or 'niece' ...
also, i would advise u to try and spend less time with the kids...
if u see them every day... try and make it so that u only see them 4 times a week... tell them u've gotten really busy with work and u can't see them as often...
and keep trying to cut it down all the way to no more than 2 times a week...
i think that way she will get more used to NOT having you around and hopefully she will spend more times with her friends.
i would suggest you to tell her mom to put her in some kinda club...
maybe a dance club? or swimming club now in the summer maybe? or if she likes any sports? maybe volleyball or tennis?
u know i think that way she will be able to socialize more, she will be able to make more friends... and also doing some kinda activities she will be able to keep her mind occupied whether she likes it or not... u know what i mean?
she's only a 10 years old, she's infatuated with u... she probably thinks of u as a mother, but at the same time she knows that u r not her mother so she loves all the attention she gets from you... this is a really difficult situation, i don't think that you staying away from her will solve anything... she will miss you, she will want to be with u so badly, that she may get depressed... i don't think she deserves u to be cold to her or show in any way that u don't love he so that she gets disappointed -again she will get depressed- so i think that the best way to handle this situation is to show her all ur maternal/auntie kinda love to her... but as she is infatuated with u, i think it would be best to make her understand that u can't spend as much time with her because of the circumstances -such as you working, and her doing different activities-
i do definitely encourage u to convince her mother so that she can get involved in some kinda club activities especially now during the summer... i think it would really help to keep her distracted, she will learn something new, she will hopefully enjoy it - i mean kids at that age usually don't like to do things like sports or stuff like that in many cases- but hopefully she will enjoy it, and i think it will also help her to socialize with other people...
and try not to do absolutely anything with her mother in their presence even if they are sleeping or whatever.. u never know if they could wake up or something... i would advise that u do it when she's over at her dad's -they live separately right? that's how it sounded to me as u described the situation- or find some1 who can take care of the children so that u guys can have some alone time...
but i definitely would recommend that you hold urself and not do anything... no matter how slim the chances of them catching u... if there's the slightest chance of u guys getting caught... i would say DON'T do anything AT ALL...
and also the last thing i would suggest u, is that if she's old enough and understands... i think u guys should be honest and tell her about ur relationship... i mean she's a 10 years old, i tihnk she's sure to understand... but seeing as she's infatuated with u... i would probably suggest that u would tell her later on when she shows signs that she's no longer interested in u... but if it takes more than 2 years for her to forget u... i would say resort to that... do tell her the truth... so that she can assimilate it and be able to try and forget about u...
good luck with this situation, i know it's really complicated... but i think that some of the things i've said would be able to help u out... so give my advises a try and see how it works out for u