How can I better cope or handle my trust issues in my relationship?
So it's hard to understand based on your message what the timeframe of everything has been like as far as how long the affair had gone on and how long it has been since the divorces. My general suggestion though is for you and your partner to work on two things: Communication and boundaries.
It's normal given the circumstances of your relationship for there to be a low level of trust, and probably to some degree avoiding becoming enmeshed too quickly may be healthy. Rather than viewing the lack of trust as something that must be immediately overcome, try to take the approach that you and your partner need to slowly build that trust. That's going to come from communicating how you and your partner are feeling, openly and honestly, even if that does at times create some conflict or tension. Some general communication tips are to use "I feel" statements, being objective about what is occurring that makes you feel that way, making sure you're choosing the right time and place to have these conversations, especially when both of you are calm, and listening openly so that your partner knows that you are hearing her. By the way, many couples choose to participate in couples therapy for help with communication. Having a third party present who can help guide the conversation and make sure that each individual feels heard can improve the quality of the communication and thus the quality of the relationship. So, if your partner is open to couples' therapy, that's something I would consider.
Boundaries are also so important in relationships and probably even more so given your circumstances. Her statements that she needs more time alone could be a result of her dealing with stress associated with the children, or having recently been divorced, or wanting to spend some time with friends, or simply because she's more of an introvert. Many people who are introverted would view seeing each other a couple times per week and then sometimes on the weekends as actually spending quite a bit of time with their partner, especially when also needing to take care of other responsibilities, especially children. It's also possible that she's wanting to take the relationship more slowly, not getting too close too quickly to avoid becoming hurt. Regardless of her reasonings, respecting the boundaries that she's setting can improve your relationship and actually help her to build trust as she can know that you're honoring her feelings and giving her the space that she needs.
If you have any additional questions or choose to participate in therapy, please let me know. I wish you the best of luck, and take care of yourself.