How to add custom route via EC2?

I need to route certain traffic via site-to-site VPN. This trivial thing doesn't work for me in AWS, while works fine in my test on-prem environment. For instance:

• I need to route traffic to 111.111.111.111/32 via 10.10.10.11
• I tried both adding this route to 10.10.10.10, and adding it into the VPC routing table - no results. I.e. I. don't see packets to 111.111.111.111 coming to 10.10.10.11. (I checked both using network sniffer on 10.10.10.11 and using AWS Flow logs).

Any ideas? TIA, Vitaly