I'm also a Texan in Germany, and my German's good enough that it often takes people a few minutes to notice I'm not a native speaker. (Left the US at 21, am now 44.) I definitely also have a lot of German artifacts in my spoken English at this point. At one point I was given the attempted compliment of, "Wow, your English is really good" – because I apparently
almost sound like a native speaker. ;-)
My children are 6 and 9 and we've raised them tri-lingual. They mostly sound native in all three, but their Serbo-Croatian and English have some German artifacts as well. Also their vocabulary isn't quite at the age-appropriate level in English since I'm basically the only person they regularly use it with, and if I don't use a word with them, they probably don't know it. This may start to change now that my oldest has also begun reading books in English. (That went surprisingly quickly; once he started with English classes in the third grade, within 3-6 months, he no longer had a definite preference for books in German over English.)
The trap to be careful of is if your family language is German that the kids eventually stop answering in their parent's language. This seems to be easier when three distinct languages are in play, possibly. Since I speak English with their mom (Serbian), there's less pull towards the "outside" language (German). Oddly, the language the speak with each other has remained Serbo-Croatian. I'd always expected that to eventually change to German, but seems unlikely at their current ages. We mostly attribute this to them having sometimes spent several weeks alone with their grandparents in Serbia when they were young, and that being the only time they only spoke a single language for up to a month, and that having solidified it as their preferred language.