Alternate Hreflang Problem

[Izzet]

We have two travel websites.
One in English language for people living in the UK.
One in Turkish language for people living in Turkey.

The major difference is:
English (UK) website shows 4+ nights accomodation prices because UK travellers never come for less than 4 nights.
Turkish website shows 1-night, 2-night, 3-night prices because Turkish travellers never stay for more than 3 nights.

We are using rel="alternate" hreflang="x" tags properly on our two websites.

Today, I am disappointed to see Google display the wrong result.

When a user in Turkey searches a Turkish keyword on Google.com.tr;
Google is showing the English language website.

When I click on Search Settings > Language;
I see that English is selected under this question:
"Which language should Google products use?"

This is a big problem for us.
Many rich users in Turkey, who are more willing to buy our services, speak English fluently and they may choose to use Gmail in English.

But we are losing business because these Turkish customers don't convert at all on the Enlish (UK) website because of the reason I explained above.

1) What can we do?
2) If we remove the rel="alternate" hreflang="x" tags now, will it hurt any of the websites?
We have seen an increase in Google rankings for the Turkish language website after using rel="alternate" hreflang="x" tags.

Izzet

[OlegKorneitchouk]

Keep the hreflang tags but add your own layer of verification.

Look up the visitor of the country and redirect to the proper version of the site.

Google looks at hreflang as guidelines and sometimes doesn't follow it perfectly.

[Izzet]

Thank you Oleg.

This partilly solves the problem.
Google will still show English title and the click-through rate from the SERPs will be relatively much lower.

I guess the only way to solve this is to remove the hreflang tags, but I have some concerns.