How to make Apache output packets through a certain network interface when connected to VPN?

So you need both default gateways; then the way to do this then is with route rules:

1) Add a secondary IP to eth0 - ie 192.168.1.7 and restart apache (sounds like your config is listen 0.0.0.0:80 so you'll just need to restart apache to get it to listen on the new IP.

2) Change the Nat rules on your router to foward traffic to this IP:

3) Create a new default route in a secondary route table lets name the table 'apache':

echo "1 apache" >> /etc/iproute2/rt_tables

4) Add a default route to this table via your local router.

ip route add default via 192.168.0.1 dev eth0 table apache

5) Finally you need a rule to define which traffic should use the apache route table.

ip rule add from 192.168.0.7 table apache

192.168.0.7 is a secondary IP and Apache is the only process using it this rule should only match the traffic leaving apache in response to web requests. This will ensure that only that specific traffic will be use the new route table and it won't mess with your VPN traffic or its current routing behaviour.

please note that the ip commands won't persist after reboot. To make them persistent add them to your interface up scripts to make run every time your laptop reboots.

P.S Leaving my old answer and did this as a new answer as this is very different solution.

Managing 2 default routes and getting some traffic to go via one and some to go via the other is a big pain and I would recommend you avoid it if possible. If you don't want to access the internet via the VPN then your setup can be greatly simplified which would solve the issues. Do you really need to access the internet via the VPN? also whats the significance of 10.132.1.5 I don't get why your using it to route to other hosts in 10.132.1.x ? you already have an IP in that subnet 10.132.1.x and should be directly connected.

so IF you don't want to access the internet via the VPN and there is no need to route via 10.32.1.5 you could simplify your routing table down to:

default via 192.168.0.1 dev eth0  proto static  metric 100 
10.132.1.0/24 dev tun0  proto kernel  scope link  src 10.132.1.6 
169.254.0.0/16 dev eth0  scope link  metric 1000 
192.168.0.0/24 dev eth0  proto kernel  scope link  src 192.168.0.6     metric 100 

Which will also solve the apache issue. Why only those routes? firstly:

10.132.1.0/24 dev tun0  proto kernel  scope link  src 10.132.1.6 

should be the only route you need to get to all the hosts on the other side of the vpn. As this route matches 10.232.1.0 - 10.232.1.254 if there are other 10.x.x.x address on the vpn network you could broaden the route to 10.0.0.0/8 If you don't understand what the /8 /24 bits mean I highly suggest you read What is the "slash" after the IP? or google for "CIDR notation". will make the /32 /1 bit make more sense.

these old routes put together define your default route via the VPN

0.0.0.0/1 via 10.132.1.5 dev tun0 
128.0.0.0/1 via 10.132.1.5 dev tun0

Breaking it up into 2 routes (one for the first half of the internet and the 2nd covering the rest) means that they have higher priority because they more specific than your default route:

default via 192.168.0.1 dev eth0  proto static  metric 100 

The problem then is that you now need to explicitly add routes that are even more specific, to force traffic via your local router(192.16.8.0.1).

123.4.5.6 via 192.168.0.1 dev eth0 
234.5.6.7 via 192.168.0.1 dev eth0 

Without the default route via the VPN those routes aren't needed. If you do need to route traffic via 10.232.1.5 and need to keep to sets of default routes I'd recommend using route rules instead of overriding the default route. Route rules are more flexible but generally how you do it is to match source IP to default gateway, so all traffic sourced from your VPN IP(10.1.232.6) goes vis the VPN default route and all traffic sourced from your local IP(192.168.0.6) uses your ISP as the default route. see https://unix.stackexchange.com/questions/22770/two-interfaces-two-addresses-two-gateways for a guide on how to do that.