Tbh with you OP, I don't really know what to say. On one hand I guess you know that your daughter is going to have sex anyways...but on the other I just can't get my head around any teen actually wanting to have sex whilst their parents are in the house or even the fact that you're okay with them having sex whilst you're there
. Even now I wouldn't dream of having sex with my DH whilst my parents were in the house. Is it not awkward getting up in the morning to find your dd boyfriend there?
I'm torn on this. You seem to have taken responsibility by putting your dd on the pill and it's nice that you have such an honest and open relationship with her but are you sure she's ready? I know she came to you for advice but what if you'd turned around and said 'I think you're too young, it's best if you wait' rather than going along with her. She may well have actually been hoping you'd said something like that because she felt she wasn't ready but may have felt pressure to do it.
Then again, I lost my virginity when I was 15. I was ready and I didn't regret it then and I don't regret it now. I could have waited another three months until my 16th birthday but I wanted to do it then. Three extra months wouldn't have suddenly magically made me more mature. I'm glad I did it when I did. So she may well be like me, feel ready and hopefully won't have any regrets.
Also, to whoever said I would change her contraception to something other than the pill, I completely agree. I would change it to something more reliable, like the implant. With the pill it's so easy not to take it properly, forget to take, take it at the wrong time, vomit it back up...whereas with the implant once it's in it's in for three years and you don't have to worry about contraception for that time.
Birth control failure rates
The pill has the highest failure rate, the implant has the lowest. You'd want to go for the most effective you could I'd imagine, assuming you don't want to be a grandmother yet 