@Frode Fuglestad you can check this document and I believe this will help you in this case : web-sites-integrate-with-vnet
However, as per my understanding you have configured VNet gateway integration, you are using Point to Site from Function to the VNet Gateway and then onto Site To Site, so lets focus on the On-premises resources section of the document and we need to consider two points as highlighted:
In this scenario you will be using the IP Address from the VNet Subnet that the Function app is allocated to as the Source IP and not the Public Outbound address.
e.g. In the subnet you can have a small address range to check ( in the screenshot it has 6 ips in that range - small range has been used for testing purpose but you need to choose the range according to the architecture) . In the destination resource, with the help of netmon trace you can verify the source ip. [Note : this is tested with regional VNet integration]
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