3 yr old urinating in house and digging back yard

My husband and I have a 3 yr old Jack Russell named Jax. He is a sweet little guy and we love him as if he were our child, but he can drive us nuts at time. Two things going on that we need some help with. Last May he started marking all over the house so we finally had him neutered in July or August. That was a huge help. But he still seems to have an accident(urine)a couple/few times a week. Any ideas? He knows to go outside and potty. In fact I take him iour in the morning before leaving for work and several time throughout the evening before going to bed at night. We need help with this. Cleaning up urine is getting very old. The other thing is we have a fenced in yard and Jax has started to dig at fence edges and also our patio edge. There is a corn field right behind our fence in the back and since the corn has been cut down, field mice have burrowed holes next to patio and outsed fence next to house foundation, so I think he smells them and wants to dig to get them. We are worried that he will get out for one. But filling in holes is not soemthing that we want to keep having to do. We are thinking about getting one of those electric/battery collars to train him not to dig. Any advice.

We would appreciate any help.