Rome and Le Marche) in 12 days? Can we also fit in Lucca?

Yes to all your questions, ha ha!
There is no one correct answer, only by looking over maps (I use google maps to get a general idea, but viamichelin is reputed to have more accurate drive times) and spending some time with train schedules (on the trenitalia) website, will the correct answer for you reveal itself.
You have given yourself ample time in Rome. I can tell you have an inclination to visit the off the beaten path places, and that is highly rewarding. If you make the journey to Le Marche, I'd say go all in. I am just starting to plan a visit there in May. I am having a really hard time figuring out out how to allot 10 days. Have you already booked return flights? Have you checked for an Ancona outbound flight?
If you are coming form the UK, you are fortunate to have cheap flights to Italy often, so I would save Pisa-Lucca-Tuscany.

One other thing to add. I think it would be prudent to take a train from Rome to one of the cities in or near Le Marche. I am just guessing that the driving may be tough--but this is just a guess, so verify that. There also could be some road closures from the earthquakes. Viamichelin may have some info on that. Once you get to le Marche, then you could rent a car--rather than having to traverse the country. That seems easier to me.
Whatever you end up choosing will obviously affect the plan, with Ubino more to the north and AP to the south.

Thanks so much for your reply! Just to clarify, I don’t live in the UK...I live in California, US...but husband is British and we’re traveling to UK after Italy.

I’m sure I just need to dig in and research this further and really appreciate the above suggestions! That said if anyone has done this trip and can suggest an itinerary/route that was successful for you, I’m all ears! Thank you!

If you've never in Italy, you need to read this. And download their free PDF.

https://www.italybeyondtheobvious.com/dont-mess-with-ztl-zones

Le Marche is one of the least traveled areas by Americans. The reason is it's difficult, is the time it takes to connect some of the towns, without driving 2-3 hours. Especially the two you wish to see. Ascoli Piceno is a beautiful village. Much more complete than San Gimignano
and far quieter. For lodging here look at Antico Borgo Piceno. Their balcony room has a fantastic view of the towers.

If you decide to skip this area, you would drive from Rome to Urbino via Spoleto and Assisi both beautiful towns to visit. Travel time without stopping in either on the way is about 3 1/2 hrs.

You could stop in Spoleto on your way and visit Assisi from Urbino.

Ok, so in doing some research and looking at flights to the UK, Bologna is my only option for flying out of the Le Marche region if leaving on July 12th. So, I've come up with two possible scenarios

Option 1:
July 6th: Rent a car (one way) in Rome & drive from Rome to Ascoli Picente (about 2.5 hour drive it seems - shorter distance than driving to Urbino)
July 6th-8th Spend time in Ascoli Picente and explore surrounding area from that base

July 8th-12th - Drive up to Urbino (about 1.5 hours) and explore surrounding area from that base
July 12th - Leave Urbino early morning, drive to Bologna (about 2 hours), drop off rental, catch flight from Bologna to UK (11am flight, 2 hour drive to Bologna from Urbino)

The cost of a one-way car rental from Rome to Bologna is about $400 during that time period (not sure of extra fees). Not sure of cost of Petrol and tolls for all that driving from Rome to AP to Urbino to Bologna though!!

Option 2:
July 6th - Take train to Bologna from Rome (2 hour train Ride), rent car in Bologna, drive from Bologna to Ascoli Picente (about 3.5 hours of driving). This is about 7 hours of travel time (maybe more!).

The rest is the same as above, only cost of rental car is slightly less, more like $329.00. Still lots of driving but slightly less only more travel time on 1st day.

Option 3:
Same as Option 2, except don't go as far as Ascoli Picente, and just have Urbino as home base. Or maybe Urbino and an agrotourismo in the vicinity of Urbino, but not traveling as South as Ascoli Picente unless I feel like doing more driving. Potentially least amount of long distance driving - but will this get boring in 5 days?

I guess I have to decide which option is best for me...but from this Forum, I'm wanting to hear - Is 5 days in Urbino too much or would you recommend other home-bases in the Le Marche Region, closer to Bologna so I'm not doing SO much driving? Or is Ascoli Picente super-duper worth seeing to where Option 1 and the additional cost of car rental/driving is worth it if I can swing it financially?

Oh wait, just saw this comment: "If you decide to skip this area, you would drive from Rome to Urbino via Spoleto and Assisi both beautiful towns to visit. Travel time without stopping in either on the way is about 3 1/2 hrs." So that sort of answers my question re: Option 3 (or option 1 if just driving to Urbino from Rome instead of to AP) unless someone else has another idea!

Le Marche is one of the least traveled areas by Americans.

Gerri, I consider this statement to be a big reason to travel there! In fact, we are in the early stages of planning a trip by train originating in Venice, stopping in Ascoli Piceno for 2 nights, then on to Apulia in the heel of the boot, basing in Bari or Polignano a Mare for another few days. Can't wait.

OP, you might want to vet this out, but there appears to be a Flix bus (flixbus.co.uk) with a straight shot from Roma Termini station to Ascoli Piceno that takes only 3 hrs, 30 min. Even I could stand the bus for that short period of time. Then you can fly out of Bologna after taking a train from Ascoli Piceno to Bologna, with a change in Ancona, with each leg of that trip being around 90 minutes, not too bad.

Enjoy your planning!