Open source wallets to host on our website
With all due respect, the first answer that you received to this question is wholly inaccurate.
'Bitcoin Core' is a client (not a library or a wallet).
You're looking for something like 'BTCPayServer', which is a completely autonomous, self-hosted wallet solution that requires a server to spin and allows you to control every aspect of your interaction with the source code on a granular level with as much fine tuning as you desire.
Here's the site: https://btcpayserver.org/
There's a live demo for you to play with along with a wealth of documentation.