Focus on the sounds that most betray an English accent: the hard g/ch, rounded vowels like uu and eu, and sentence intonation. You can improve noticeably in a few months with daily, targeted practice using free resources and honest feedback from your partner.
Start by identifying your specific weak spots. Record yourself reading a short Dutch sentence, then compare it to a native speaker's version (use Forvo or YouTube clips). The Dutch g (as in "goed") and ch (as in "lachen") are produced from the back of the throat, not the front like English. Practice by gargling sounds. The uu sound (like in "muur") is a tight, rounded front vowel, not like English "you". Listen to minimal pairs: "buur" vs "beer". Intonation in Dutch rises and falls more than English, especially at the end of questions and statements. Mimic short phrases from a series like "Zeg het in het Nederlands" on YouTube.
Use free apps like Speechling (limited free version) or the pronunciation modules on Duolingo (ignore the rest) for repetition. The key is getting real-time feedback. Ask your partner to correct you on just the three worst sounds for 5 minutes daily. She can also give you a short list of phrases you will definitely use: "Leuk jullie te ontmoeten", "Dank u wel", "Het eten is heerlijk". Practice these until they feel automatic. Accept that you will still have an accent, but showing effort matters more than perfection. Your future in-laws will appreciate you trying, even if it's not flawless. Avoid rushing; speak slowly and clearly. One concrete next step: today, pick 5 phrases, find their pronunciation on Forvo, and repeat each 20 times while recording yourself. Compare weekly.
Tradeoffs: You won't sound native in a few months, but you can become understandable and respectful. The biggest risk is focusing on vocabulary instead of sounds. Prioritize the g/ch, vowels, and rhythm over learning many new words. Your partner is your best resource, so use her feedback actively.