How to communicate with my wife when she is already overwhelmed?

Hi there. Thank you so much for this question. You have provided information that supports why this would be such a complicated situation. That said, I want to take this question by parts as there is a variety of areas in need. Please note that this is a limited answer that requires much more time and words to cover. Either way, I truly hope that what I provide in my message today will be a good reference for you moving forward. Perhaps it will encourage you and give you support on your journey ahead. 

Let us begin. I want to start with your main question: how you communicate with your wife. As a mental health counselor I always say: context really matters. The communication style of your relationship matters and how you manage inner conflict matters. There are multiple moving parts, even the smaller day-to-day ones, that can all add up as a barrier for communication. When I say "communication" I am referring to deeply intentional, actively listening, emotionally safe conversation. If this is not already a regular practice, it might not feel fully clear on how to move forward. A lot of the time many couples come in just wanting to be listened to. Creating space where active and reflective listening is involved can really increase the quality of conversation. Many couples I work with can tend to turn away from their partners for various reasons. Perhaps they are concerned they will burden their partner, they feel shame for what they want to talk about, they might not have skills that make it more simple to open up, they are in denial of the issue at hand, there is conflict avoidance, trust is not the foundation to make a conversation even work, or they might be stonewalling their partner. Sometimes, partners might try to soothe by partaking in other activities, such as watching TV, going shopping, playing video games, and otherwise. This is not a complete lists as there are many other dynamics and/ or factors that can be taking place. 
Ask yourself this: What is a barrier in our relationship that creates walls and causes us to turn away instead of towards one another? 
As you peel back the layers of this you might realize what is actually taking place in the actual marriage that causes distance, which leads to realizing that it is not just about what she went through that is a factor here. Recognition of this can help you both practice new behaviors that can change the culture of communication. Counseling can help you both gain skills needed for communication.

I also really advocate for checking in at least weekly. Setting a date and time, if possible due to your schedules, can be very fruitful. This time is not just a "date" but more so a time where you both turn towards one another without distractions. It can, in fact, be a date, but could also be a time to build more understanding for one another. This could be by finding meaningful games to play, checking in on how the other is doing, partake in an activity together that helps you bond, etc. Over time, using these check ins can give you space to explore your concerns as well. Before a check in both parties need to work on their own self, coming into their check in time ready to be undistracted and completely present mentally, emotionally , and physically to the other. Having this routine can increase connection, communication, and quality time together. 

It also sounds like you both could benefit from learning each other's love languages. This is merely a framework for getting to know what your partner perceives as loving. It's a good start to a relationship that is more curious about the other and more attuned to the other's needs. It also makes the needs more mutual than one sided. From what I perceive in your message, there is a need for words of affirmation. It seems like you want to hear that she acknowledges you for being a good father and husband, as well as a very hard worker, as you said. It was not by coincidence that you added that portion to your question. It seems pretty clear that you are ready to communicate more with her, but want to be mindful of her feelings as well. However, that is not a reason to override the needs in the relationship long term. You both benefit from this as well. 

I also want to add the importance of you both having a neutral outlet. Seems like you both have to put in independent work to be more present in the relationship. Similarly, your wife can really benefit from her own neutral outlet as well. Working with a trauma informed counselor can really help with gaining perspective, validation, and clarity. Feeling overwhelmed, struggling with self image, self esteem and worth, and trust issues is not to be taken lightly as this can very directly and negatively impact the marriage and her long term mental health. 

I wish you both the best moving forward and hope that this information provided here today will encourage you to keep moving and stay curious. Always remain open to help on how to work through this. Thank you again for your question and I hope this has been a helpful guide for you. Thank you for wanting to better your marriage and quality of life. I think your eagerness for change will be good fuel for committing to the process. Thank you!