First your lawn - if your dogs are bitches, yes, that will cause brown patches in your lawn. If you allow them to pee there, the only way to obviate this is to immediately hose down the patch they've just made to dilute the urine. Male dogs usually cock their legs and burn your plants instead.

As its now almost July, it would be better to wait till autumn to plant your rose, then its got less chance of drying out at the roots and dying, but you can plant it now, provided you're prepared to keep it well watered.

Again thank you bamboo good advise yes they are girls I haven't a hose so will a watering can do ?? My rose happy in pot if I do put in garden and water a lot will it live ..x

Yes, it will live in the ground, the rose I mean, but if you haven't a hose, I would definitely wait till autumn to plant it.

Couple of cans of water on the lawn when its been used might help, but even hosing off isn't a perfect solution. You could try creating an area where the dogs are allowed to wee, and prevent them from using anywhere else.

There's a thing, Dog Rocks I think it's called, which you put in their water dish to stop the problem (the dogs, not the rose).
I would check first with the vet that it's not a gimmick or harmful though.