You have to kill the grass first or the fragments will sprout after it is tilled. If moles have ruined the existing lawn then they will probably get into the new lawn too, so unless you also exterminate the moles first putting much effort and expense into another lawn may be questionable. And then you must hope a bunch of new, replacement moles don't show up.

Tree roots in the existing lawn will get chewed up if a tiller or other digging equipment is run through them. This is not desirable. Consider spending a little money on a garden consultant, landscape designer or garden coach to view the site and help you figure these things out.

I'm no lawn/grass expert, but here's what happened in my
garden.

When I bought my house, the whole lot was covered in a mixture of grass and weeds. I dug out the grass where I wanted beds, built some 2x4 edging for borders around the beds, and trucked in lots of new top soil.

In one area where I wanted a nice lawn, I removed all the old grass and weeds, added fresh topsoil, rented a roller, and applied seed. The grass came up, but I also got more weeds than I had before! I then stripped the area (again) and put down bark. This is where I now have a large table and chairs. I thought that having the furniture on lawn would be a problem - the furniture would have to be moved for every mowing. However, sitting on an area that is barked meant getting wood chips and dust in my shoes and socks, so I put a rug down under the furniture area. I must redo (maybe a wood deck) as the bark with carpet is not the best solution.

In the other areas where I wanted lawn, I filled in any low spots with new topsoil right on top of the lawn with a wheelbarrow and shovel, and watered the 'holes' a lot. I never reseeded. The grass grew up through the new topsoil (and spread in from the sides of the holes). I used a very good quality weed & feed fertilizer for two years. The grass is now lush, the weeds are gone, and the lawn is flat (and it was cheap and easy).

What I learned: that improving an existing situation is sometimes better than starting over from scratch.

Daphne in Tacoma

I had my front yard redone last year. The company killed the old grass, tilled the yard added 3 inches of compost and built 40 feet of cedar fence for 3 grand. I don't know how much cheaper I could have done it but they were done in two days and it looks great. About a month after the new lawn was put in I started getting some serious mole problems. All I can say about dealing with the moles is go to Lowes or Home Depot and buy a few traps. It's a war of attrition.

Thanks for your replies... we have considered filling in the low spots, but we also have HIGH spots!! That and the probable network of old mole tunnels underneath is what makes me think we need to rototil to break it all up.

My main concern is damaging the existing tree/shrub roots, but perhaps we can only rototil through the main area.

We need to do this as inexpensively as possible, unfortunately.

Here is a link that might be useful: Yard