You also mentioned "doesn’t allow me easy access my private key", can you still get it though even if you have to jump through hoops?
So, I did some more digging... signed up for a dummy account... and noticed there is a "Backup" option. This lets you download an encrypted wallet file... which downloads as "coinpunk.txt"
Further investigation shows:
https://github.com/kyledrake/coinpunkA, now defunct and no longer maintained/developed, DIY web-wallet service... so it looks like bcoiner.com is simply a rebadged version of coinpunk.
The "good" news, is that I was able to decrypt the "coinpunk.txt"... and it showed this:
{
"keyPairs": [
{
"key": "5JRuzjmgty9hdzrs4Woqj76MmejwR4jkTTk6NsfzbFFnXXnDfNd",
"publicKey": "0cc68cb0b0addf94b1b683ec757b4ba3a5e5bdf5",
"address": "12AYxmYbob7qGjP86YLNwZsFhZzRqj7BjA",
"isChange": false,
"name": "Default"
}
],
"transactions": [],
"unspent": []
}
I checked the private key using bitaddress.org, and the key matches the address... So maybe it IS possible that the OP can recover their coins. They'll need to be quick and try to recover them before that other transaction confirms tho!
So, maybe it seems that it is not that bcoiner.com is a scam as such, but possibly it is just full of security flaws allowing hackers to steal wallet files/passwords, get the private keys and then steal peoples coins?