In my family, we often speak in one language and answer in another. Sometimes the same speaker will switch tongues in the middle of a conversation, or even in the middle of a sentence.
There’s a reason I work as a translator. I’ve been training for it from childhood.
One of my great-grandfathers spoke South Dakota, another, Massachusetts. Only slight accents were evident, and I have no anecdotes. Carry on.
My grandmother left Sweden back in the 20’s. She came to Chicago and got a job as a baby nurse. She had some Swedish friends near where they lived and one of the men in that group of friends taught her some English. The people who she worked for also spoke Swedish, but were fluent in English. One day, they were having a tea party (or something similar) and they found out that my Grandmother had learned some English. She was SO proud! They asked her what words she had learned, and the word that her “friend” had taught her was “Bullshit”.
We moved to the US from Germany when us kids ranged in age from 5 to 10. We moved here in June and in September started right into school. Luckily us kids picked up quite a bit of English during the summer. We used to translate for our parents. They both had jobs, so they also learned to communicate fairly quickly, but had really heavey accents and mixed German words with English. Our neighbors and my Dad’s workmates used to get a kick out of hearng him swear up a storm in German. One time he got upset at Dairy Queen cause he ordered “eis” and they gave him a cup of ice instead of ice cream. My Aunt, who had sponsored us and had moved here a few years before we did, still calls a garbage can a “cabbage can”. I enjoyed listening to my parents’ accent and it didn’t bother me at all. Oh, and my grandkids call me Opa. 
As an interesting aside, my husband’s grandmother was Swiss and a native speaker of Swiss German. He spent whole summers with her when he was young. She raised dogs (schnauzers, naturally! :D) My husband loves dogs and tagged along with her underfoot from toddlerhood to pre-teen while she did things with the dogs at the beach where she lived.
He speaks no Swiss German, no regular German from his Grandfather who escaped the Nazis and refused to speak it. They spoke English at home and to the kids (different homes, they divorced, but still.) His father, therefore, speaks no Swiss German or regular German either.
However, whenever my husband speaks to our dogs, he has a 50/50 chance of whatever he says to them being in English if he’s not really paying attention. If he is, it’s in English. If it’s an absent minded “get down!” or “stop that” it’s just as likely to be in Swiss German as it is in English. Apparently Gran never bothered speaking English to the dogs!
Cracks me up every time.
My mother spoke excellent English before she came to the US in the early 1950’s, but she never quite lost her accent. I don’t recall it embarrassing me much, at least not a much as some other things she would say or do, but that is another thread ;). She wrote in the sütterlin style of handwriting that everyone in the US found utterly incomprehensible. I had to read and interpret every note she ever sent to my school. Only later did it occur to me to interpret her writing…loosely.
I don’t actually speak very much German but I can understand, and read, a surprising amount. I do remember occasionally questioning myself at the last possible second if the word I was about to use was German or English, (spatula? how the heck is that an English word?) but I don’t recall any spectacular incidents, so all must have been well.
Another factor was that my sisters and I grew up in a military town. Foreign-born mothers were not uncommon in the community we grew up in.
When we would visit Germany, I remember that my mom had a little bit of difficulty switching back to speaking German full-time. If she couldn’t instantly remember the German word, she’s unconsciously substitute the English word. This would quickly resolve and within a day or two, it was German only. the same thing would happen in reverse, upon our return to the US.
My dad was born in Mississippi; he and my mother met at an Air Force Base in Frankfurt. One of my favorite “foreign language” stories is about him. Dad learned a few phrases in German but was never fluent. He always said if you knew how to order ham and eggs, a beer, and how to say “I love you” in the local language, you could travel anywhere. Anyway, apparently dad went to a grocery store to buy some bottles of beer. He negotiated the sale successfully, then the clerk said something he didn’t understand. Dad didn’t want to appear ignorant, so he just said “ja, ja” (yes, yes.) The clerk whipped out a bottle opener and popped the caps off every bottle of beer! Dad told this story on himself for years.
Not parents, and not immigrants, but rather in-laws visiting us in the US from their home in Malaysia (they speak English fluently, but Tamil is their first language) –
One day during their visit, they walked downtown and decided to buy some tee-shirts at a place that sold them really cheaply.
On tee-shirt they purchased was printed with the words “MUFF DIVER” (and a generic sport-diving logo). The other read “WANNA HUMP?”, with a picture of a camel.
Poor things! They had no idea, obviously. My wife and I weren’t sure if we should be angry at the clerks who sold them the shirts, or impressed at their “customer is always right” attitude.
Anyway, the store went out of business not long after. And my hip, young, good-humored diving-enthusiast cousin was happy to get the first shirt (I think the other one became a rag.)
My sort of stepdaughter’s Turkish mum speaks English pretty well. However she seems to have a mental block when it comes to understanding that she’s going wrong with certain common phrases. For example she says “too many” when she means “a lot” so there are “too many daffodils in the park” or “too many beaches near where her parents live”. Her Dad used to get worried that his daughter would copy her and make the same mistakes but I’m sure her peers will put her right.
My paternal grandparents were Russian immigrants to the US. They always managed to live in whatever Russian enclaves they could find. So growing up, my dad had little or no exposure to English.
When they sent him to kindergarten at age 5, he still spoke only Russian. (I guess my grandparents thought that he would be taught English there.) He was sent home that day with a note that said, “Yevgenie cannot speak English. Please send him back to school once he learns it.” After about a year (with a tutor, I suppose), he went back and continued his education.
Speaking to my dad, you’d never guess that English was his second language. (I think he was a little embarrassed about it all.) He’d only speak Russian to his mother, especially when he was upset about how much she spoiled us grandkids.
My favorite ‘Dad struggling with English’ stories.
We were watching tv when the news came on that Richard Burton died. My Dad was a fan. I can’t say this is verbatim, but his comment went like this:
‘Ach, such a shame. He was such a good actor, not like the no-talent dummies you see today. And he was so young - at the *pinochle *of his career’ (while rolling around on the floor tears running down my face, I explained the word was ‘pinnacle’).
Another time, he was talking to my sister’s friend. She had a choice of someone paying her back a loan of $50 now, or waiting a week and getting $60. Dad was telling her to go for the sure thing now, because ‘…a bird in the pocket is worth 2 in the trees’ (I have no idea if this is the Czech version of the expression we’re familiar with).
Heh.
My parents once met with the mayor of Istanbul. They were talking about the Jewish community in Turkey when the mayor said, “Istanbul has many Jews. *Too *many Jews!”
Having some experience with English as a second language, they were not offended.