mygui.m

window = figure('units', 'normalized', 'OuterPosition', [0 0 .5 .5], ...
  'Name', 'My Gui', 'NumberTitle', 'off', 'MenuBar', 'none', ...
  'Toolbar', 'none', 'HandleVisibility', 'off');
% Main panel.
mainpanel = uix.Panel('Parent', window, 'Padding', 2, ...
  'BorderType', 'none');
tabgroup = uitabgroup('Parent', mainpanel);
% Make the tabs.
tab1 = uitab('Parent', tabgroup, 'Title', 'Tab1');
tab2 = uitab('Parent', tabgroup, 'Title', 'Tab2');

%% Make the first tab.
tab1_main = uix.HBox('Parent', tab1, 'Spacing', 3);
tab1_left = uix.Panel('Parent', tab1_main, 'Padding', 2);  % left side
tab1_right = uix.Panel('Parent', tab1_main, 'Padding', 2);  % right side
tab1_left_plot_container = uicontainer('Parent', tab1_left);  % container needed for plot
tab1_left_axes = axes('Parent', tab1_left_plot_container);
tab1_right_plot_container = uicontainer('Parent', tab1_right);
tab1_right_axes = axes('Parent', tab1_right_plot_container);
% Adjust the layout. 
set(tab1_main, 'MinimumWidths', [300 300]);

%% Make the second tab.
tab2_main = uix.HBoxFlex('Parent', tab2, 'Spacing', 3);
tab2_left = uix.Panel('Parent', tab2_main, 'Padding', 2);  % left side
tab2_right = uix.Panel('Parent', tab2_main, 'Padding', 2);  % right side
tab2_left_plot_container = uicontainer( ...
  'Parent', tab2_left);  % container needed for plot
tab2_left_axes = axes('Parent', tab2_left_plot_container);
tab2_right_plot_container = uicontainer('Parent', tab2_right);
tab2_right_axes = axes('Parent', tab2_right_plot_container);
% Adjust the layout.
set(tab2_main, 'Widths', [100 -1]);
set(tab2_main, 'MinimumWidths', [300 300]);

The problem

You can adjust the border in the second tab from the first tab. All you have to do is: while on first tab, find with the mouse exactly where the adjustable border on the second tab lies (somewhat tricky to find at first), then you can adjust this border from the first tab like so: