Connecting to internet through VPC peering

Question

I have two custom VPCs for Private & public access: VPC1(private) & VPC2(public). Each VPC has one subnet and further one EC2 with proper inbound rules. I can update software in public EC2 which is fine. Also, I can establish an SSH connection between those two Ec2 after VPC-peering. But my goal is to use the internet on PVT EC2 via public EC2. To achieve that I must add the NAT-gateway of VPC2 onto the Route table of VPC1(if I am not wrong). However, the NAT gateway is not visible on the VPC2-route table. Though, I can use NAT-gateway from private subnet to public subnet in the case when both subnets are within a single VPC. But, here I am struggling when they are in two different VPCs. Any advice, please?