Thanks for info
Firstly: Reading from logs it seems you do NOT have mixins installed:
java.lang.ClassNotFoundException: org.spongepowered.asm.launch.MixinTweaker
ModularUI2 depends on mixins library (preferbly Unimixins) this is NOT a conflict with CofhCore you simply need to install Unimixins or other libraries this mod depends on for more info read GitHub - GTNewHorizons/ModularUI2: ModularUI from GTCE but cleaned up...
Secondly: even if this was a conflict I cannot help if this is a ModularUI’s problem this is unrelated to my mod you should contanct their devs not me!
Also for next time please use sites like pastebin to send a log SPECIALY on froums! its always good not getting a headache from the spams! 
and lastly please use the issue froum in github instead of froums, as you can see it took 10 days for me to see your message! i would reach out to you much sooner if an issue was opened on github! as i will recieve an email asap. 
goodluck