When i import the WIF key into another wallet, it instead imports the corresponding Legacy address (beginning with D) instead of the Segwit address.
Since WIFs don't have the address type information inside, you have to find a way to tell the wallet you are using what type of address it should derive. This is a wallet specific thing that you should ask the developers of that wallet or users of it.
Are my funds gone forever, or is it possible to access them?
Most probably you'll have a hard time reclaiming them but they aren't gone.
Try checking out the
https://coinb.in/#newTransaction section of the website and try to create a transaction spending your coins by entering your redeem script in the first box and setting a destination address.
Then sign it using the
https://coinb.in/#sign page with your private key.
If it's not possible to access, why does coinb.in even offer segwit as an option in the first place?
You really shouldn't use this type of tools for anything serious though, specially if you used it online. They are usually complicated and for "advanced" usages, not to mention could have vulnerabilities.
Try to stick to wallets.