Pi-hole's Conditional Forwarding should have three entry fields:
Local network in CIDR notation, IP address of your DHCP server (router), Local domain name (optional).
It should work straight away, provided your separate VLANs subnets can be aggregated into a common top level network (like a 10.10.0.0/23 would cover 0.10.0.0/24 and 10.10.1.0/24).
And of course, your router must be able to answer DNS requests for local hosts - not all routers do so. Check with nslookup <local-name> <router.ip> before you experiment with CF.
If your VLANs are on different ranges (like 192.168.0.0 and 10.10.10.0 subnets) and/or do have different local/search domains, you'd have to follow jfb's suggestion and create a custom dnsmasq configuration file.
Though it's in German, you may refer to my recent Conditional Forwarding mit mehreren DHCP Servern? - #2 by Bucking_Horn for some suggestions. Searching our forum may quite possibly yield English samples as well. 