Average diesel for a Class A for a year - take the number of miles you expect to drive X 1.25 divide that by 8 mpg - times $4.50 per gallon.
A 'Four Corners' Trip across the country is likely 13,000 miles shortest route - say 16,250 miles on the MH - 2,030 gallons of fuel adds up to $9,135 for fuel. Add $2-5,000 for maintenance needs.
If you average 350 miles per driving day - which is 7 hours at a 50 mph average - you will spend 47 days driving. That leaves 318 days to see the country. You will need 36 days for laundry, shopping, other maintenance tasks. 282 free days. On that basis you might be able to make about 47-48 stops for a week each.
Camping costs - commercial campgrounds - daily fee average $40 if you are not looking for top resort locations and getting weekly rates - $14,600. If you want full services - Raise that by 25% - 50-75% if you want to visit resort type RV parks.
You can lower the camping costs with discounts such as Good Sams, Passport America - or the very best - if you are over age 62 - stay at federal campgrounds for half price or a deep discount. But many will not have 50Amp hookups, relatively few will have sewer hookups. Two of you in a MH should be able to go a week between visits to the dump station if you are moderately conservative with water usage.
However, size of your rig might be an issue. A big 40 footer isn't going to fit into a lot of federal parks or state parks in many places.
Food - while you can eat cheap while stopped in a CG - most folks retirement age don't want to skimp too much. Count your food costs to be 10-15% higher than they are today.
Additional costs - entertainment - a satellite dish program will cost about the same as what you have at home. Internet might be more costly with less bandwidth/ capacity and speed. Some places neither internet nor cell phone will be available.
Phone - I assume you both have cell phones and that won't change.
Laundry - something we don't consider as a cost - but if you don't get a washer/dryer in the rig - it will add a couple twenties to your monthly costs.
Big question - are you keeping the house/ home?
If you sell out, your base camping costs with internet and satellite TV will likely be at or below your current housing costs. But if you keep the house - your camping costs are all additional.
Since you are talking about a one year tour - I assume you are keeping the house, but not renting it out.
Another issue - medical costs/ coverage. Make sure your policies cover you far from home. Not even considering the changes happening in that area - a lot of folks don't have policies which provide coast to coast coverage.
Sounds really expensive doesn't it?
But the number of ways to lower the costs is huge:
Take three years - and the $9,000 in fuel drops to something closer to $3,500 per year - because you will be able to stay where you find something interesting for longer. You won't have to rush to 'finish'. You might find you want to go to Alaska one summer.
Plan to spend two weeks at a weekly rate if you can in one location - but always ask about the cost of electricity. Some places include electricity in weekly rates - some bill you by the KWH. Almost all RV monthly rates are for separately billed electricity.
Don't visit big cities unless you really, really want to. Costs are higher. Rediscover rural / small town America.
Visit the 'big' tourist attraction areas on the shoulder seasons - before or after the prime season.
There are literally thousands of couples and singles crossing this country every year living on less than $30,000 and having a great time. It can be done even cheaper with some planning and cash conservation.
Don't get me wrong - money makes it easier and a strong financial reserve gives you less worry. Being debt free is the greatest freedom you can have.
However such a trip is the adventure of a life-time - and you don't want to wait too long before you start.
From your question - I assume you don't currently have a DP MH - so that is the first task - find out if you really like living in a MH on the road. If you don't have RV experience - I would suggest a rental for one or two weeks.
Yes, expensive - but cheap in the long run.