i think you are all leaving yourselves wide open for charges with guns near a public footpath and toting baseball bats again near a public footpath
I agree with Robert, in this case you would be classed as the agressor (sp?). guns are not allowed withing a certain distance of a right of way.
many 'Public spaces' have a dog control order on them, £1,000 fine. Check with your local council. Try and get a photo or video of her not cleaning up. You could always stick the pictures up for all to see what a lazy dirty b****r she is!
how about running a length of plain wire alongside the bridleway, then about a foot of so into your land run an electric fence (suitably labelled) round the inside perimeter, then see if the dog tries to get through twice!