That's not how Stipe and similar services work. They exist to prevent your scenario. They actually work very similar to Paypal except that you don't have to be

That's not how Stipe and similar services work. They exist to prevent your scenario. They actually work very similar to Paypal except that you don't have to be redirected to the Paypal site to enter your credentials. Instead you get a small "secured by Stripe" widget that takes the credentials (directly to Stripes PCI compliant servers so that yours don't have to be). As a reply you'll get some kind of token that you can use to actually charge the credit card (or SEPA, or whatever else). It's a secure way of handling payment without the "we're now redirecting you to some payment site" which BY THE WAY Paypal themselves offer in the form of their Braintree payment services.