I think that making it through Divine Liturgy can be tough even on the kids who have a generally positive attitude towards going to church ... I think there are some adults who have trouble as well!
The length of the service and the repetition of certain prayers is challenging for those who are not used to it or who just aren't in the right frame of mind for it. At the little Mission Church where I am a member, the younger children are excused for Sunday School immediately after Divine Liturgy, although it is not uncommon to see parents step out with their restless children at other times as needed. You said your church is small ... does it have a Sunday School? Sometimes a little enjoyable interaction during Sunday School is enough to redeem an otherwise boring morning in the eyes of a 5 year old. If your church does not have a Sunday School, it seems like you have a vested interest in helping to start one! It may not be a replacement for Divine Liturgy, but it can really help with the motivation factor.
Also, I know that there are plenty of people on this forum who are going to vehemently disagree with me, but I'm going to say it anyway: maybe you need to arrive sometime after the beginning of Divine Liturgy and before the very end, at least until your son's attitude improves. Your priest may show some flexibility in this matter, considering your circumstances.
It sounds like it's starting to become a battle of wills, which is generally a lose-lose situation, but as much as possible try to stay positive with your son when talking about going to church. It isn't necessarily going to be a fun experience for him, but between the two of you maybe you can figure out some ways to make it more positive. If lighting a candle or two helps to do that, then so be it. I liked some of Ialmisry's other thoughts as well, including praying for friends at church and prayer time at home. Shanghaiski had some good ideas too, such as drawing icons and finding ways to get your son involved. Also, a little reasonable bribery ... er, reward ... might also be in order, such as agreeing to stop somewhere for a treat afterwards if his conduct is satisfactory. Sometimes that works ... sometimes. One thing I'm pretty sure does not work is taking a heavy-handed, authoritarian approach with a strong-willed child.
Another thought ... are there any particularly approachable parents there at church who you could talk to about your concerns? They know your church and are hopefully at least acquainted with your family, so they are in a better position than the people on this forum to give you truly useful advice.
Your son's Muslim father may be a factor in all of this, even if it isn't overt. He knows his father isn't Christian, much less Orthodox, so even if the dad doesn't say anything about it, just knowing that does not help to get your son to church. Nevertheless, he is with you, and you have to try to give him the best religious education that you know how to.
It sounds like useless platitudes, but the main thing for you during this difficult period is to try to be patient, not only with your son but also yourself and your own religious path. When kids are involved, sometimes you can't make progress as fast as you would like, but the main thing is knowing the right direction for you and your family and being persistent in continuing to go in that direction. Also, try to be flexible, even if the people around you aren't.
Kids delight in breaking inflexible parents! I pray for your perseverance, that you do not let yourself become discouraged or deterred. Please forgive me if these comments are not helpful!