However, I don’t want to use a bitcoin wallet service which I would build from scratch myself or hire a developer to do it for me, instead, I would prefer if I’m able to integrate an existing reputable Bitcoin wallet service provider (e.g. Bitgo, Blockchain, Coinbase e.t.c) in my website.
If the integration is possible, I would not have to worry much about securing the users Bitcoin wallets on the site against hackers, making sure the users' wallets are secured would be the problem of the Bitcoin wallet service provider I'm using. I, the website owner/admin, don't want to have access to the users' wallet without their permission, I believe this integration will enable me to achieve that as well.
I welcome replies that answethe r this question or ideas that are better than what I'm asking. Thanks
Thank you for the final remark - the fact you are concerned with the safety of your customers fund is encouraging.
AFAICT, you could use something like BitGo, but still you are still trusted to orchestrate transactions which take place between users. What if you lied one day?
I have a suggestion. Don't offer a wallet. Securely accept with seller recipient addresses, and have buyers pay directly to them. With bitcoin, if you're the platform, it's possible to avoid handling the coins in any capacity. This is the only safe way to not let your people down.
Wallets are not designed to be integrated anywhere. Leaving OAUTH2 credentials which can call the 'sendMoney' API call... you're gonna have a bad time. (worse, I've seen bitcoin wallets offering static API keys for use in integrations. I wept.)