Might be a case of paying for childcare (if you can) and getting something really small for now. If not, maybe wait until they’re a bit bigger because I’m pretty sure children won’t be allowed as it’s not safe
I had close personal friends that were artists and would let me bring my baby but that's different. I just got into tattooing myself, it's cheaper 😬 also, in incognito we have no idea where you live, every shop is different but if you don't know anyone on a personal basis I doubt they'll let you bring the baby.
I don't know any tattoo studios that allow kids in I'm afraid, it might be an insurance issue? You can always message a few and ask in case.