The context for this question should have been "at its intended location." Will you be able to network the Mini via Ethernet when it's installed at its final resting place? (I'm guessing the answer is "no"; just want to confirm.)
So the BOLT isn't near the router, then, which would allow it to be networked via Ethernet? (Again, just need to confirm.)
Ok, a cable-capable BOLT; then the BOLT is capable of making a network connection as a MoCA client, same as the Mini. (The OTA-only "BOLT OTA" model lacks any built-in MoCA functionality.)
Since you're not using a combo cable gateway with a built-in MoCA bridge to set up a MoCA network, you'll need to add a MoCA adapter at the modem/router location, to act as the MoCA/Ethernet bridge (effectively to act as the MoCA access point).
My recommendation would be the goCoax MoCA 2.5 adapter ($60 at Amazon
As for getting it installed/connected, the aim is to bridge between the home coax plant and the router's Ethernet LAN. So, you can either connect the MoCA adapter's "MoCA" port to the wall outlet, and connect the modem via the adapter's "TV" port; or, you may want to use a 2-way splitter to get both the modem and MoCA adapter connected directly to the coax. (Just cap the MoCA adapter's "TV" port if unused/open.) If you try using the pass-through for the modem's connection, you might want to check the effect on the modem's connection if power is cut-off to the MoCA adapter.
Either way you go with the coax, the MoCA adapter's "LAN" port will need to be connected via Ethernet to a LAN port on the router.
You'll end up w/ something similar to the following:
Could hardly be easier. You'll need to get a "PoE" MoCA filter
installed on the input port of that splitter, to keep your MoCA signals inside the home (and to efficiently reflect the MoCA signals back onto your coax plant), and you'll want to make note of the splitter model # and its specs. If you have issues getting MoCA working, you may want to upgrade the splitter to a unit recommended for MoCA 2.0/2.5, such as the Holland GHS-3PRO-M
The final configuration may be similar to the following (YMMV):
The BOLT and Mini would simply be configured as MoCA clients once everything's connected.
p.s. About that switch in the last diagram, see >this post<
for info on extending wired networking via a MoCA-client TiVo DVR's otherwise-unused Ethernet port.