For those who disagree with the OP's dd having an implant - why? Is it really any worse than the pill? The implant is one of the most reliable forms of contraception out there (if not the most reliable). With the pill you can forget to take it, not take it properly, get ill and vomit it up, be on antibiotics which can effect it...with condoms they can split, you can not put them on properly, etc. And this happens to adults too, not just to teenagers so it's unfair to say that you're not mature enough to have sex if you can't remember to take the pill or put a condom on properly. With the implant it's there and you don't have to remember anything. Many GP's and family planning clinics are now promoting the use of long term reversible contraception (such as the implant) especially for teens because of the reasons I outlined above.
Somebody who is old enough to understand and consent to the consequences of having an implant is also old enough to learn how to use condoms properly.
There are far more minimal side effects to condoms, and they protect from STIs. If your DD does not learn how to use condoms now, and get into the habit of insisting a sexual partner uses them, at what point is she going to learn this?
Has anybody said they won't be using condoms? It's possible to have the implant and use condoms you know. It doesn't have to be one or the other. Many people will be on the pill/implant/injection/coil but will double up with condoms both as a secondary contraception as well as protection against STI's. I still do this. I know several other people who do too so it can't be that unusual.
I would never encourage condoms as the only source of contraception though. If it was my dd I'd much prefer she was the pill/implant/injection (but I'd prefer injection or implant again for the reasons mentioned above) and was using condoms as an additional method. Never condoms alone though.