We recently completed a DYI bathroom redo. We had the bathtub in for awhile and would use it occasionally even though we had yet to install the toilet or sink. Never had any problems. Once the toilet was installed, problems started. First it would back up, or the bathtub would. We would take the toilet off and fix pipes underneath. Toilet goes back on, and problems come back. We have had the septic pumped and the lines flushed out, still that has not helped. My husband has gone under the mobile home several times trying to find a place in the lines that could be the problem. Now it is even worse, when the washing machine drains, it backs up into the bathtub as well as when the dishwasher drains.
We are beyond frustrated. Can anybody please help and advise?

First you need to determine where the problem is. Is there an outside cleanout in the sewer pipe ? The problem is either inside or outside, possibly from debris entering the sewer pipe during the remodel. There's probably cleanouts under the home that will allow you to run a sewer cleaning machine thru the pipe to remove any obstruction.

It doesn't sound like an obstruction as much as a venting issue ?????? When the toilet is off everything drains ok??? If so then when you set the toilet it backs up?????? If that's the case it sounds like you need to add a vent to the outside atmosphere or at least a mechanical vent aka studdor vent very common in mobile homes or manufactured homes???? Take a look at venting !!