@Mike,
As others are saying, most ISPs do allow remote access via mobile data etc, it’s just a case of configuring it cortectly. It seems unlikely that an ISP would restrict email to their own network; In this age of mobile devices, they’d lose too many customers.
If you care to name your ISP, and the mobile device you want to use (iOS I assume?), more specific advice might be forthcoming,
@Ronski...
I had this issue years ago so simply used Gmail to send and set the appropriate email return address. Since using a proper hosted email service its not an issue.
... I used to do likewise, in days of old. But I’d not recommend it these days, as mail sent with a spoofed or unexpected return address may be flagged as spam, hence might never reach the recipient, and the sender may never know it failed. Note the “mays” and “mights” meaning, in effect, “sometimes and sometimes not”.